THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 


PRESENTED  BY 

PROF.  CHARLES  A.  KOFOID  AND 
MRS.  PRUDENCE  W.  KOFOID 


y 


y,  del. 


WATERSPOUT  OBSERVED   OFF  THE   COAST   OF   SOUTHERN    SICILY   IN  AUGUST,    1876. 

Frontispiece. 


A    POPULAR  TREATISE 


ON  THE 


WINDS 


COMPRISING   THE 

GENERAL   MOTIONS   OF  THE  ATMOSPHERE, 

MONSOONS,   CYCLONES,   TORNADOES, 

WATERSPOUTS,  HAIL-STORMS, 

ETC.   ETC. 


BY 

WILLIAM  ^ER^EL,  M.A.,  PH.D., 

LATE   PROFESSOR  AND  ASSISTANT  IN  THE  SIGNAL  SERVICE,   MEMBER  OF  THE  NATIONAL 

ACADEMY  OF  SCIENCES  AND  OF  OTHER  HOME  AND   FOREIGN 

SCIENTIFIC  SOCIETIES. 


Eontron 
MACMILLAN   AND  CO, 

1890 


/7 


FERRIS  BROS., 

Printers, 

326  Pearl  Street, 

New  York. 


QcKl 


PREFACE. 


SINCE  the  middle  of  the  present  century  great  advances 
have  been  made  in  meteorology,  especially  in  the  study  of  the 
mechanics  of  the  atmosphere.  Before  this  epoch  little  was 
known  even  with  regard  to  the  general  motions  of  the  atmos- 
phere, the  true  theories  of  cyclones,  tornadoes,  water-spouts, 
hail-storms,  cloud-bursts,  etc.,  were  entirely  unknown,  and  the 
observed  phenomena  were  mostly  regarded  as  mysteries.  Al- 
though there  are  still  some  things  which  require  more  study 
and  further  explanation,  yet  these  subjects  have  now  become 
much  clearer  and  better  understood  ;  and  so  great  has  the 
change  been,  that  the  recent  advances  are  often  called  the  "  new 
meteorology." 

During  this  period  of  advancement  the  writer  has  had  pub- 
lished a  number  of  meteorological  papers  in  an  endeavor  to  ad- 
vance our  knowledge  in  the  subjects  mentioned  above.  The 
first  of  these,  entitled  "  An  Essay  on  the  Winds  and  the  Cur- 
rents of  the  Ocean,"  was  published  in  the  Nashville  Journal  of 
Medicine  and  Surgery  in  the  year  1856.  The  writer's  attention 
was  first  directed  to  this  subject  by  reading  Maury's  Physical 
Geography  of  the  Sea,  from  which  he  learned  that  the  pressure 
of  the  atmosphere  is  less  both  at  the  poles  and  at  the  equator 
of  the  earth  than  it  is  over  two  belts  extending  around  the 
globe  about  the  parallels  of  30°  north  and  south  of  the  equator. 
An  attempt  to  account  for  this  phenomenon,  which  was  then 
inexplicable  upon  any  known  principles,  resulted  in  the  essay 
named  above.  This  essay  was  mostly  of  a  popular  character, 
and  only  a  very  imperfect,  though  at  the  time  important,  first 
step,  which  subsequently  led  to  further  researches,  and  the  dis- 
covery of  the  effect  of  the  earth's  rotation  in  the  dynamics  of 
the  atmosphere,  which  has  served  to  clear  up  many  of  the 

iii 


M37345O 


IV  PREFACE. 

mysteries  of  the  older  meteorology.  This,  essay  was  subse- 
quently republished  by  the  Signal  Service  in  Professional  Paper 
of  the  Signal  Service,  No.  XII. 

In  the  year  1858  this  subject  was  again  taken  up  by  the 
writer,  but  treated  in  a  very  mathematical  manner,  and  the  re- 
sults were  given  in  a  paper  entitled  "  The  Motions  of  Fluids  and 
Solids  relative  to  the  Earth's  Surface,"  which  was  published  in 
a  series  of  parts  in  Runkle's  Mathematical  Monthly,  and  subse- 
quently republished  by  the  Signal  Service  in  Professional  Paper 
of  the  Signal  Service,  No.  VIII,  with  extensive  notes,  giving  the 
mathematical  processes  in  detail,  by  Professor  Frank  Waldo, 
then  in  the  Signal  Service. 

This  subject  was  taken  up  a  second  time  by  the  writer  a 
number  of  years  afterward,  but  still  treated  in  a  very  mathe- 
matical manner,  and  the  researches  so  extended  as  to  embrace 
cyclones,  tornadoes,  water-spouts,  hail-storms,  cloud-bursts,  etc. 
This  resulted  in  his  "  Meteorological  Researches  for  the  Use 
of  the  Coast  Pilot,"  published  in  three  parts  in  the  Reports  of 
the  Superintendent  of  the  Coast  and  Geodetic  Survey  for  the 
years  1875,  1878,  and  1881. 

In  his  "  Recent  Advances  in  Meteorology,"  published  as  the 
second  part  of  the  Chief  Signal  Officer's  Report  for  1885,  the 
writer  went  over  the  same  ground  again,  but  adopted  mathe- 
matical methods  somewhat  simplified  and  gave  further  exten- 
sions of  the  more  popular  parts  of  the  subjects. 

Although  these  papers  have  been  pretty  widely  distributed 
as  Government  publications,  yet  they  have  fallen  into  the  hands 
of  comparatively  few  of  the  large  number  of  readers  who  are 
interested  in  the  important  subjects  of  which  they  treat,  and 
they  are  also  too  mathematical,  for  the  most  part,  for  many 
readers.  On  account  of  the  great  and  pretty  general  interest 
which  has  been  taken  of  late  years  in  meteorological  subjects, 
there  are  now  many  who  wish  to  obtain  at  least  a  general, 
if  not  a  thorough,  knowledge  of  the  most  important  princi- 
ples of  these  subjects,  but  who,  either  from  lack  of  ability  or 
time  and  inclination  to  take  hold  of  difficult  reading,  are  de- 
sirous of  having  some  more  popular  presentation  of  them,. 


PREFACE.  V 

and  the  desire  has  often  been  expressed  that  the  writer 
would  undertake  such  a  presentation  of  these  subjects,  treated 
mostly  in  a  mathematical  way  in  the  papers  referred  to.  To 
comply  with  this  desire,  so  far  as  the  nature  of  the  subjects 
treated  will  admit,  is  the  object  of  the  present  work. 

From  the  nature  of  the  subjects,  however,  little  can  be 
done  where  even  the  simpler  operations  of  mathematics  are  en- 
tirely discarded,  and  the  results  of  such  a  method  of  treatment 
would  be  very  unsatisfactory  to  a  large  class  of  readers  who 
have  some  knowledge  of  the  simpler  principles  and  operations 
of  mathematics,  so  that  these  have  been  used  in  the  work ;  but 
all  that  could  well  be  done  has  been  done  in  the  way  of  mere 
verbal  explanations  and  illustrations  of  the  subjects.  It  is  there- 
fore thought  that  the  work  can  be  read  with  profit  by  those 
who  are  deficient  in  even  the  elementary  principles  of  mathe- 
matics. 

In  the  present  more  popular  presentation  of  the  subjects 
treated  in  the  works  referred  to  above,  of  course  the  methods  are 
very  different,  and  the  whole  matter  is  very  much  expanded,  so- 
that  all  has  been  rewritten  except  a  few  pages  in  the  chapter  on 
Tornadoes,  which  have  been  copied  with  little  or  no  change 
from  my  "  Recent  Advances  in  Meteorology."  In  the  mathe- 
matical treatment  of  the  subjects,  where  this  has  been  intro- 
duced, no  claim  is  made  to  elegance  of  methods,  and  sometimes 
simple  arithmetical  methods  are  used  instead  of  algebraic 
methods  and  the  calculus,  such  as  almost  any  one  well  versed 
in  the  higher  methods  of  analysis  frequently  adopts  in  the  first 
discovery  of  important  principles  and  results,  or  which  he  may 
use  as  a  check  of  results  obtained  in  a  more  mathematical  way, 
the  principal  object  being  to  give  some  insight  into  the  sub- 
jects, though  in  a  homely  way,  to  readers  who  have  little  facil- 
ity ia  the  use  of  mathematics. 

The  subject-matter  contained  in  the  following  pages^  is 
mostly  an  expansion  of  a  series  of  forty  lectures  delivered  by 
the  writer  before  a  class  of  army  officers  of  the  Signal  Service 
during  the  months  of  February  and  March,  1886,  in  which  the 
manner  of  presentation  of  the  matter  was  somewhat  the  same 


VI  PREFA  CE. 

as  that  adopted  here.  This  was  necessary,  since  the  members 
of  the  class  had  no  time  for  reading  and  study,  and  so  for  en- 
tering into  the  matter  more  thoroughly,  for  all  their  time  not 
given  to  the  hearing  of  the  lectures  had  to  be  given  to  their 
daily  work  in  the  service. 

A  thorough  knowledge  of  the  principles  contained  in  the 
following  work,  it  is  thought,  will  be  of  great  advantage  to  all 
who  are  desirous  of  understanding  the  observed  phenomena 
and  sequences  of  the  weather,  and  of  forming  rules  for  weather 
prediction,  and  especially  to  the  seaman  on  the  ocean  in  the 
management  of  his  vessel.  For  although  no  attempt  has  been 
made  to  lay  down  detailed  rules  to  be  followed  in  the  various 
cases,  yet  the  principles  are  given  and  explained  by  which  each 
one  with  a  knowledge  of  them  can  intelligently  form  his  own 
rule  in  any  case,  which  is  generally  much  better  than  to  blindly 
follow  rules  which  can  rarely  be  given  so  as  to  cover  all  cases 
without  exceptions. 

So  much  interest  is  now  being  taken  in  meteorology  that  its 
principles  must  soon  be  taught  to  a  considerable  extent  in  our 
colleges  and  universities,  and  it  must  form  a  part  of  any  course 
in  Physics  where  a  separate  chair  is  not  assigned  to  it.  It  is 
therefore  thought  that  lecturers  on  meteorological  subjects  be- 
fore college  classes,  or  any  general  and  larger  audiences,  will 
find  much  in  the  following  work  which  can  be  advantageously 
and  conveniently  used. 

The  author  is  indebted  to  the  courtesy  of  the  Chief  Signal 
Officer  for  permission  to  copy  from  the  publications  of  the  Sig- 
nal Service  a  few  of  the  illustrations  contained  in  the  following' 
pages. 

He  is  also  indebted  to  the  kindness  of  his  friend  Professor 
Frank  Waldo  for  the  full  and  well-arranged  index  to  this  work. 

WM.  FERREL. 

KANSAS  CITY,  Mo.,  April,  1889. 


CONTENTS. 


CHAPTER   I. 

THE  CONSTITUTION  AND  NATURE  OF  THE  ATMOSPHERE. 

SECTION 

I  Composition  of  the  Atmosphere, I 

2-3  Boyle  and  Mariotte's  Law, 2 

4  The  Law  of  Charles  and  Gay-Lussac, 3 

5-8  Arrangement  of  the  Constituents, 4 

9-13  Pressure  of  the  Atmosphere, 9 

14-16  Aqueous  Vapor  of  the  Atmosphere, 16 

17-27  Dynamical  Heating  and  Cooling  of  the  Air 20 

28-31  Stable  and  Unstable  Equilibrium, 34 

32  Relation  between  Changes  of  Altitude  and  Density, 39 

33  The  Viscosity  of  the  Air, 40 

CHAPTER  II. 

THE  MOTIONS  OF  BODIES  RELATIVE  TO  THE  EARTH'S  SURFACE. 

34  Introduction, 42 

35-40  Centrifugal  Force, 42 

41-43  The  Principle  of  the  Preservation  of  Areas, 54 

44-46  Centrifugal  Force  in  Motions  on  the  Earth's  Surface,   ......  59 

47-49  The  Principle  of  Equal  Areas  in  Motions  on  the  Earth's  Surface,  .  65 

50-51  Resultants  of  the  Two  Forces  and  Motions,    ........  71 

52  Where  the  Centre  of  Force  is  not  the  Pole,    ..,,.*..  75 

53-60  The  Deflecting  Force  of  the  Earth's  Rotation, 77 

CHAPTER   HI. 
THE  GENERAL  CIRCULATION  OF  THE  ATMOSPHERE. 

61-67  Introduction, 89 

68-69  Distribution  of  Temperature  over  the  Earth's  Surface,     ....  98 

70  Distribution  of  Aqueous  Vapor, 101 

71-73  General  Circulation  without  Rotation  of  the  Earth, 102 

74-82  General  Circulation  with  Rotation  of  the  Earth, 106 

83-89  Comparisons  with  Observations, 121 

v 


VI  CONTENTS. 

SECTION  PAGE 

90-96  Effect  of  the  General  Motions  upon  Atmospheric  Pressure,  .     .     .  133 
97-99  East  Velocities  deduced  from  ^Pressure  and  jTemperature    Gra- 
dients,       145 

100-103  Surface  Winds,  Calms,  and  Calm-belts 149 

104  Summary  and  Graphic  Representation  of  the  Motions  and  Pres- 
sures,       .,     .     '. 154 

105-109  Annual  Oscillations  of  the  Calm-belts, 156 

CHAPTER   IV. 
CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION. 

no  On  the  Relative  Climates  of  the  Lower  and  Higher~Latitudes,  .     .  163 

TH-I2O  Wet  and  Dry  Zones, 164 

1 21-122  Relative  Temperatures  of  East  and  West  Sides  of  the  Continents,  .  179 

123-128  In  Connection  with  Mountain  Ranges, 183 

CHAPTER  V. 
MONSOONS,  AND  LAND-  AND  SEA-BREEZES. 

129-136  Introduction, 193 

137-145  The  Monsoons  of  Asia  and  the  Indian  Ocean 200 

146-147  The  Monsoons  of  Africa, 212 

148-149  The  Monsoons  of  North  America, 214 

150  The  Monsoons  of  South  America, 217 

151-152  Land- and  Sea-breezes, 219 

153-154  Mountain  and  Valley  Winds, 223 

CHAPTER  VI. 

CYCLONES. 

155  Introduction, 226 

156-165  Vertical  Circulation, 227 

166-172  Gyratory  Motion  of  Cyclones, 241 

I73~I74  Atmospheric  Pressure  in  Cyclones, 251 

I75~I76  Resultant  Motions, 255 

177  Surface  Calms, 257 

178  Graphic  Representation  of  Motions  and  Pressures, 258 

179-183  Comparisons  with  Observation, 261 

184  Gradual  Enlargement  of  Cyclones, 273 

185-191   Progressive  Motion  of  Cyclones, 275 

192-193  Veering  and  Backing  of  the  Wind  and  Changes  of  Pressure  and 

i. Temperature, 287 

194  Cyclone  of  August  2,  1837,  at  St.  Thomas 292 


CONTENTS.  vii 

SECTION  PAGE 

195  Manilla  Typhoon  of  November  5,  1882 295 

196  Cyclone  of  Cienfuegos  on  September  5,  1882, 297 

197-199  Rain  and  Cloud  Areas  in  Cyclones, •.    .     .  298 

200-205  Resultants  of  Cyclonic  and   Progressive  Motions 303 

206-207  The  Eye  of  the  Storm, 311 

208-209  Secondary  Cyclones, .     .     . 315 

210-212  Stationary  Cyclones 318 

213-216  Cold  Waves  and  Northers, 322 

217  Pamperos, 329 

218  The  Mistral  and  the  Bora, 331 

219-220  The  Foehn  and  the  Chinooks, 332 

221  The  Sirocco, 336 

222-226  Cyclones  with  a  Cold  Centre, 337 

227-228  Areas  of  High  Barometric  Pressure, 342 


CHAPTER   VII. 
TORNADOES. 

229  Introduction, 347 

230-231  The  Conditions  of  a  Tornado 348 

232-237  Gyratory  Velocity  and  its  Effect  on  Pressure,  .  .  .  ."  .  .  .  353 

238-243  The  Energy  of  a  Tornado, 362 

244-258  Force  of  the  Wind  and  Supporting  Power  of  Ascend  ing  Currents,  .  371 

259-261  Resultants  of  Gyratory  and  Progressive  Motions 395 

262  Rainfall  in  Tornadoes, 399 

263-271  Waterspouts 401 

272-276  Hail-storms, 420 

277-281  Cloud-bursts, 429 

282-283  Fair-weather  Whirlwinds  and  White  Squalls 434 

284-292  Where  Tornadoes  are  most  likely  to  Occur, 437 

293-294  Sand-spouts  and  Dust- whirlwinds, 443 

295  Blasts  of  Wind  and  Oscillations  of  the  Wind- vane, 446 

296  "  Pumping  "  of  the  Barometer, •    .     .  448 

CHAPTER  VIII. 

THUNDERSTORMS. 

297  Introduction, 450 

298-302  Observed  Phenomena, 450 

303-309  The  Theory 459 

310-311  Relation  between  Thunder-storms  and   Cyclones 467 

312  Annual  and  Diurnal  Inequalities 470 

APPENDIX 473 

INDEX 481 


THE   WINDS. 


CHAPTER  I. 
THE  CONSTITUTION  AND  NATURE  OF  THE  ATMOSPHERE. 

COMPOSITION   OF  THE  ATMOSPHERE. 

1.  THE  gaseous  envelope  surrounding  the  earth  called  air, 
and  regarded  as  a  whole,  the  Atmosphere,  is  composed  of  the 
two  principal  gases  in  its  constitution,  oxygen  and  nitrogen, 
together  with  a  small  amount  of  carbonic  acid  and  traces  of 
other  gases.  These  constitute  what  is  called  dry  air.  When 
composed  of  oxygen  and  nitrogen  only,  it  is  said  to  be  dry  and 
pure.  In  addition  to  the  constituents  of  dry  air  the  atmosphere 
contains  also  a  variable  amount  of  aqueous  vapor,  which,  in  a 
warm  climate,  may  amount  to  one-twentieth  part,  or  more,  of 
the  whole.  The  proportions  of  dry  air,  neglecting  the  slight 
and  mostly  unmeasurable  traces  of  the  other  constituents,  may 
be  put  as  follows :  Oxygen,  20.95  ;  nitrogen,  79.02 ;  and  car- 
bonic acid,  0.03  parts,  in  100  by  volume.1  * 

The  constituents  of  the  atmosphere  are  not  chemically  com- 
bined, but  exist  together  as  a  mechanical  mixture.  If  the  at- 
mosphere were  perfectly  at  rest  each  constituent  would  assume 
the  same  status  and  distribution  as  it  would  if  the  others  were 
not  present.  Each  one,  therefore,  would  form  an  atmosphere 
of  itself,  independent  of,  and  unaffected  by,  the  others.  This 
arrangement  of  the  constituents  is  called  Daltons  law.  But  as 
perfect  quiet  for  a  long  time  is  a  condition  of  this  arrangement, 
on  account  of  the  almost  continual  agitations  of  the  atmosphere, 
this  law  is  never  satisfied. 

*  For  the  references  see  the  Appendix. 


2      CONSTITUTION  AND  NA  TURE   OF   THE  A  TMOSPHERE. 

BOYLE  AND   MARIOTTE'S   LAW. 

2.  Gases  are  extremely  elastic,  so  that  a  given  amount  of 
any  one  of  them  may  be  compressed  into  a  space  almost  infi- 
nitely small ;  and  if  the  pressure  is  sufficiently  removed,  it  ex- 
pands into  a  space  almost  infinitely  great.  The  space  which  a 
given  amount  of  gas  occupies  under  varying  pressures  and  tem- 
peratures is  its  volume  ;  and  the  space  which  a  unit  mass,  as 
one  gram  or  one  grain,  occupies  under  an  assumed  standard 
pressure  and  temperature  is  called  the  specific  volume.  The 
standard  pressure  is  that  of  the  mercurial  column  of  the  barom- 
eter 76omm  in  height  at  the  temperature  of  o°  C.,  and  subject 
to  the  action  of  the  force  of  gravity  at  sea-level  on  the  paral- 
lel of  45°;  and  the  standard  temperature  is  that  of  melting  ice. 

If  we  let  P  represent  the  pressure  and  Fthe  volume  of  any 
given  amount  of  gas  at  any  temperature,  then,  however  much 
the  pressure  may  vary,  the  temperature  remaining  the  same,  we 
have  sensibly  the  product  PV  equal  to  a  constant.  The  law 
represented  by  this  expression  is  called  Boyle  and  Mariottes 
law,  from  the  names  of  its  two  independent  discoverers,  of 
whom  Boyle  seems  to  have  been  the  first. 

If  we  let  P0  represent  the  standard  pressure,  as  defined 
above,  and  F0  the  specific  volume  of  the  gas,  we  have,  what- 
ever may  be  the  pressure, 

PV—  P  V 

—  •*•  o  *  o  > 

in  which  Fis  the  volume  of  unit  mass  at  standard  temperature 
of  o°C.  when  subject  to  the  pressure  P. 

According  to  Boyle  and  Mariotte's  law,  whatever  the  tem- 
perature of  the  gas,  if  P  is  doubled  Fis  reduced  to  one  half,  or 
if  P  is  diminished  to  one  half  Fis  then  doubled,  and  so  for 
any  other  ratios,  either  integral  or  fractional ;  and,  consequently, 
if  P  is  infinitely  great,  F  becomes  infinitely  small,  and  vice  versa. 

The  elastic  or  expansive  force  of  a  gas,  which  in  a  static 
state  of  the  gas  is  exactly  equal  to  the  pressure,  arises,  according 
to  the  kinetic  theory  of  gases,  from  the  action  of  the  atoms 
or  molecules  upon  one  another  and  upon  the  sides  of  the  con- 
taining vessel  in  their  numerous  contacts  in  flyingx-with  very 


THE  LAW  OF  CHARLES  AND   GAY-LUSSAC.  3 

great  and  differing  velocities  in*  all  directions.  The  molecules 
of  different  gases  at  the  same  temperature  have,  on  the  average, 
different  velocities  ;  and  as  the  forces  are  as  the  squares  of  the 
velocities,  different  gases  have  different  elastic  forces  and  vol- 
umes under  the  same  conditions  of  pressure  and  temperature. 

3.  The  law  of  Boyle  and  Mariotte  is  not  strictly  true  for 
any  of  the  gases,  or  for  the  atmosphere  regarded  as  a  simple 
gas  ;  and  this  is  especially  the  case  where  the  pressure  is  either 
extremely  great  or  extremely  small.     According  to  Regnault's 
experiments,  the  product  PV  in  the  case  of  the  atmosphere  de- 
creases with  increase  of  pressure  up  to  the  pressure  of  about 
65  atmospheres,  after  which  it   increases,  and  for  very   great 
pressures  it  becomes  much  greater  than  it  is  in  the  case  of  the 
ordinary  pressure  of  the  atmosphere   at    the    earth's   surface. 
According   to   the    experiments  of   Mendeleef2  of  St.  Peters- 
burg, the  atmosphere  conforms  to    Boyle's  law  at  a  pressure 
of  about  650  millimeters  of  mercury  ;  but  for  smaller  pressures 
the  product  PV  diminishes,  and  at  very  low  pressures  the  air 
seems  to  almost  entirely  lose  its  elasticity  and  become  an  ex- 
ceedingly rare  liquid. 

THE   LAW   OF  CHARLES  AND   GAY-LUSSAC. 

4.  The  elastic  force  of  a  gas  and  of  the  atmosphere  is  in- 
creased with   increase  of  temperature.     It  is  found    from  ex- 
periment that  its  volume  increases  the  -^^  part  of  what  it  is  at 
the  temperature  of  melting  ice  for  each  degree  Centigrade  of 
increase  of  temperature.     This  is  the  law  of  Charles  and  Gay- 
Lussac,  so  called  from  its  discoverers,  of  whom  Charles  is  thought 
to  have  been  the  first.     By  this  law  the  volume  of  unit  mass  of 
gas    under  the  standard    pressure  P0  and   temperature  r   be- 
comes V0  (i  H-^-g-r).     We  therefore  have,  as  an  expression  of 
both  the  laws  of  Boyle  and  Charles  combined, 


in  which  V,  for  any  given  pressure  P,  is  the  volume  of  unit  mass 
for  the  temperature  ^ 


4      CONSTITUTION  AND  NATURE   OF   THE  ATMOSPHERE. 

By  the  law  of  Charles,  as  represented  in  the  last  member  of 
this  equation,  a  gas  would  lose  all  of  its  elastic  force  when 
cooled  down  to  273°  below  the  zero  of  the  Centigrade  scale, 
since  with  t  =  —  273°  the  second  member  of  this  expression 
would  vanish.  As  the  elastic  force  depends  upon  temperature, 
or  by  the  kinetic  theory  of  heat,  upon  the  velocities  of  the 
molecules  in  their  impacts  upon  one  another,  where  elasticity 
ceases  temperature  also  must  cease,  and  hence  at  273°  below 
the  ordinary  zero  there  cannot  be  any  temperature.  This 
point,  therefore,  is  called  the  absolute  zero,  and  the  temperature 
reckoned  from  this  point  is  called  the  absolute  temperature. 

If  we  put  T  for  the  absolute  temperature,  the  preceding 
expression  of  the  combined  laws  of  Boyle  and  Charles  in  a 
function  of  T  becomes 


in  which  R  =  -^^  P0  F0.  From  this  it  seems  that  the  pressure,, 
if  the  volume  remains  constant,  and  conversely  the  volume, 
if  the  pressure  remains  constant,  is  proportional  to  the  absolute 
temperature.  Since  different  gases  under  the  same  temperature 
have  different  elastic  forces,  and  consequently  have  different 
specific  volumes,  it  follows  that  F0  differs  in  different  gases,  and 
consequently  the  value  of  R  in  the  expression  above. 

Since  the  pressure,  and  consequently  the  elastic  force,  in  a 
static  condition  of  the  gas,  is  proportional  to  T  when  the  volume 
is  constant,  and  the  elastic  force  depends  upon  and  is  propor- 
tional to  the  square  of  the  velocities  of  the  atoms  or  molecules, 
it  follows  that  in  the  increase  of  velocities  with  the  increase  of 
temperature  the  mean  square  of  the  velocities  is  as  the  absolute 
temperature. 

The  law  of  Charles,  as  that  of  Boyle,  is  not  strictly  correct 
in  all  cases,  but  the  deviations  from  the  law  within  the  range  of 
experiments  are  extremely  small. 

ARRANGEMENT   OF  THE   CONSTITUENTS. 

5.  If  each  of  the  several  constituents  of  the  atmosphere 
formed  an  atmosphere  of  itself  around  the  globe,  the  arrange- 


ARRANGEMENT  OF   THE    CONSTITUENTS.  5 

merits  of  the  particles  with  regard  to  altitude  would  be  different 
in  the  several  gases,  so  that  the  densities  would  not  decrease 
with  increase  of  altitude  in  the  same  ratio.  Since  different 
gases  have  different  elastic  forces,  the  same  weight  of  each 
under  the  same  pressure  occupies  different  spaces,  or,  in  other 
words,  has  different  volumes ;  and  in  order  to  have  the  same 
weights  in  a  given  space  it  is  necessary  for  the  gases  to  be  sub- 
ject to  different  pressures.  As  the  density  under  the  same 
pressure  must  be  inversely  as  the  volume  where  the  tempera- 
ture remains  the  same,  the  greater  the  elastic  force  of  a  gas  the 
less  its  density.  Hence  the  greater  the  elastic  force  of  a  gas 
forming  an  atmosphere  around  the  globe,  the  higher  it  would 
be  necessary  to  ascend  to  get  above  a  certain  part  of  it,  as  one 
half  or  any  other  proportion,  and  the  more  the  whole  mass 
would  be  expanded  upward,  where  it  is  subject  to  the  pressure 
only  arising  from  the  action  of  the  force  of  gravitation  upon  its 
own  mass. 

In  the  case  of  a  gaseous  atmosphere  surrounding  the  earth 
in  a  state  of  static  equilibrium,  the  pressure  at  any  altitude 
depends  upon,  and  is  very  nearly  proportional  to,  the  mass 
of  gas  above  that  altitude,  since  the  force  of  gravity  of  unit 
mass  differs  but  little  at  the  different  altitudes  in  the  atmos- 
phere. Hence  the  density,  since  by  Boyle's  law  it  is  as  the 
pressure,  decreases  with  increase  of  altitude ;  for  the  greater 
the  altitude,  the  less  the  pressure  of  the  part  above  that  alti- 
tude. The  greater  the  altitude,  therefore,  the  greater  must  be 
the  increase  of  altitude  required  to  cause  a  given  ratio  of  de- 
crease of  pressure  of  the  whole,  and  of  the  density  at  the  earth's 
surface.  For  instance,  at  the  altitude  where  the  pressure  is 
reduced  to  one  half  of  what  it  is  at  the  earth's  surface,  it 
would  be  necessary  to  ascend  twice  as  far  to  arrive  where  the 
pressure  and  density  are  diminished,  say  the  -j-J^  part  of  what 
they  are  at  the  earth's  surface,  as  it  would  at  the  earth's 
surface.  If,  therefore,  Boyle's  law  held  for  infinitely  small 
pressures,  there  would  be  no  exterior  limit  to  such  a  gaseous 
atmosphere,  though  it  would  become  extremely  rare  at  no 
very  great  altitude.  But  if,  as  may  be  the  case  according  to 


6      CONSTITUTION  AND  NA  TURE   OF   THE  A  TMOSPHERE. 

the  experiments  of  Mendeleef,  §  3,  a  gas  under  a  very  low- 
pressure  loses  its  elastic  force  and  becomes  a  very  rare  liquid,, 
then  there  must  be  a  limit  to  such  an  atmosphere,  but  the 
density  at  this  limit  must  be  very  small. 

6.  According  to  Dalton's  law,  deduced  from  experiments,, 
and  being  also  in  accordance  with  the  kinetic  theory  of  gasesr 
each  constituent  of  our  atmosphere  in  a  perfectly  quiet  state 
would    form  a   separate    and    independent   atmosphere,    with 
exactly  the  same  arrangement  of  its  parts,  and  the  same  rela- 
tion of  the  densities  of  these  parts  with  reference  to  altitude,  as 
if  the  other  constituents  were  not  present.     The  constituents,, 
therefore,  with  the  greatest  elastic   forces  and  least  densities 
under  the  same  pressure  would  be  expanded  upward  the  most, 
so  that  whatever  might  be  the  relative  densities  of  the  inde- 
pendent gaseous  atmospheres  at  the  earth's  surface,  the  densi- 
ties of  the  more  elastic  gases  would  decrease  with  the  increase 
of  elevation  at  a  less   rate  than  those  of   the  gases   of   less 
elastic   force.     For  instance,  if    an  atmosphere    of   hydrogen 
existed  with  one  of  nitrogen,  the  density  of  the  latter  under 
the    same    pressure   and   temperature    being    fourteen    times 
greater,  and  consequently  its  elastic  force  as  many  times  less, 
if  the  densities  of  both  gases  at  the  earth's  surface  were  the 
same,   at  only  a  small  altitude   the  density  of  the  hydrogen 
would   be  much  greater  than   that   of  the  nitrogen,  since   it 
decreases  with  increase  of  altitude  at  a  much  less  rate,  and  at 
an    altitude  where    the   nitrogen    would    sensibly   vanish    the 
density  of  the  hydrogen  would  be  diminished  by  only  a  small 
part ;  and  if  at  the  earth's  surface  the  density  of  the  hydrogen 
were  very  small  in  comparison  with  that  of  the  nitrogen,  yet 
at  only  a  very  moderate  altitude  it  would  be  the  predominating 
constituent. 

7.  The  density  of  a  gas,  in  relation  to  that  of  dry  and  pure 
air  of  the  same  temperature  and  subject  to  the  same  pressure, 
is  called  its  relative  density.     The  relative  densities  of  oxygen, 
nitrogen,  and  carbonic  acid  gas  are  respectively  1.1056,  0.9714, 
and   1.52.     The   densities  and  consequently  the  elastic  forces 
of  the  two  principal  constituents  of  our  atmosphere  being  so 


ARRANGEMENT  OF   THE   CONSTITUENTS.  7 

nearly  the  same,  the  relations  between  the  densities  of  the  two 
at  the  earth's  surface  and  up  at  considerable  altitudes,  from 
what  has  been  shown,  would  not  be  very  different  if  the  two 
existed  together  in  accordance  with  Dalton's  law.  For 
instance,  the  ratios  by  volume  of  the  two  constituents,  oxygen 
and  nitrogen,  at  the  earth's  surface  being  as  20.95  to  79.02,  re- 
spectively, §  I,  there  would  be  very  nearly  the  same  ratio  up  at 
a  considerable  altitude,  the  proportion  of  oxygen  to  that  of 
nitrogen  decreasing  very  slowly.  The  density  of  carbonic  acid 
gas  being  much  greater,  and  consequently  its  elastic  force 
much  less,  its  density  decreases  with  increase  of  altitude  at  a 
much  more  rapid  rate  than  that  of  oxygen  and  nitrogen,  and 
consequently  in  the  upper  part  of  the  atmosphere  the  propor- 
tion of  this  gas  relative  to  that  of  the  two  others  would  be 
much  less  by  Dalton's  law  than  it  is  at  the  earth's  surface ;  but 
this,  we  have  seen,  §  I,  forms  only  a  very  small  part  of  our 
atmosphere.  This  compound  atmosphere,  therefore,  can  be 
regarded  as  a  simple  gas  ;  for  although  the  several  gases  "of 
which  it  is  composed  would  not  have,  if  it  were  in  a  quiescent 
state,  quite  the  same  ratios  between  them  at  the  earth's  surface 
and  in  the  higher  altitudes,  yet  on  account  of  the  continued 
agitation  of  the  atmosphere  in  its  general  circulation  and  by 
storms,  these  relations  are  so  nearly  the  same  at  different 
altitudes,  that  analyses  of  air  at  sea-level  and  on  the  tops  of 
the  highest  mountains,  and  of  samples  obtained  from  very 
high  altitudes  in  balloon  ascensions,  show  no  sensible  differ- 
ences in  the  proportions  of  oxygen  and  nitrogen.  And  as  the 
rate  of  expansion  with  increase  of  temperature  is  sensibly  the 
same  for  all  gases,  the  laws  of  both  Boyle  and  Charles  can, 
therefore,  be  applied  with  sensibly  the  same  accuracy  as  in  the 
case  of  any  simple  gas. 

8.  According  to  Boyle's  law,  the  atmosphere  with  constant 
temperature  would  occupy  precisely  the  same  volume,  however 
much  its  mass  were  increased  or  diminished.  If  the  mass 
were  doubled  or  diminished  to  one  half,  the  pressure,  and  con- 
sequently the  density,  would  be  changed  in  the  same  ratios,  and 
so  for  any  other  proportions ;  and  hence  the  volume  would,  in 


8      CONSTITUTION  AND   NA  TURE   OF   THE  A  TMOSPHERE. 

all  cases,  be  the  same.  The  densities  at  the  same  altitudes, 
however  much  the  whole  mass  of  the  atmosphere  were 
increased  or  diminished,  would  have  the  same  ratios  to  the 
densities  at  the  surface,  and  it  would  in  all  cases  be  necessary 
to  ascend  to  th*e  same  altitude  to  get  above  any  given  propor- 
tion of  the  whole.  If,  therefore,  the  atmosphere  were  of  uni- 
form temperature  at  all  altitudes  and  the  part  above  any  given 
level,  as  that  of  the  top  of  Dike's  Peak,  were  considered  by 
itself,  it  would  form  an  atmosphere  exactly  similar  to  the 
whole,  but  the  pressures  and  densities  at  equal  altitudes  above 
the  base  would  be  less,  and  in  the  same  proportion  as  the  mass 
of  atmosphere  above  that  level  is  less  than  that  of  the  whole. 
Since  the  densities  at  different  altitudes  in  an  atmosphere 
of  uniform*  temperature  decrease  in  the  same  ratio  as  the  pres- 
sures in  ascending  vertically,  and  these,  as  the  amounts  of 
atmosphere  remaining  above,  it  follows  that,  at  all  altitudes,  it 
is  necessary  to  ascend  through  the  same  vertical  distance,  in 
order  to  get  above  a  given  proportion  of  the  whole  existing  above 
the  level  of  the  starting  point.  For  instance,  if  it  is  necessary 
to  ascend  from  sea-level  to  the  altitude  of  Pike's  Peak  to  get 
above  two  fifths  of  the  whole  atmosphere,  then  it  is  necessary 
to  ascend  just  as  much  higher  to  get  above  two  fifths  of  what 
still  remains  above  that  level,  and  so  on.  Again,  if  it  is  neces- 
sary to  ascend  vertically  a  given  distance  to  get  above  one 
tenth  of  the  atmosphere,  then  it  is  necessary  to  ascend  the 
same  distance  to  get  above  one  tenth  of  what  is  left ;  and  so  on, 
ad  infinitum.  After  the  first  ascent  there  would  be  nine 
tenths  of  the  whole  mass  left  above,  and  consequently  the 
pressure  and  density  would  be  diminished  to  nine  tenths  ;  after 
the  second  ascent,  to  nine  tenths  of  nine  tenths  of  what  they 
were  at  the  earth's  surface  ;  and  after  the  third  ascent,  in  the 
ratio  of  the  third  power  of  nine  tenths,  or  in  the  ratio  of  1000 
to  729,  and  so  on.  Hence  if  different  altitudes  are  taken  in 
arithmetical  progression,  the  corresponding  pressures  and  den- 
sities diminish  in  geometrical  progression.  And  this  is  true 
whether  we  start  on  the  earth's  surface  or  at  any  level  above 


PRESSURE  OF  THE  ATMOSPHERE.  9 

It,  since,  as  we  have  seen,  the  part  above  that  level  forms  an 
atmosphere  precisely  similar  to  the  whole. 

Where  the  temperature  diminishes  with  increase  of  altitude, 
as  in  the  real  case  of  nature,  the  rate  of  increase  of  pressure  and 
of  density  with  increase  of  altitude,  relatively  to  the  whole,  be- 
comes greater  above  than  below,  and  it  is  not  necessary  at  any 
given  level  to  ascend  through  so  great  distances,  to  get  above 
a  given  proportion  of  the  whole  above  that  level,  as  it  is  at  the 
earth's  surface. 

PRESSURE  OF  THE  ATMOSPHERE. 

9.  The  pressure  of  a  body  arises  from  the  action  of  a  force 
upon  that  body  when  it  is  not  free  to  move,  and  this  pressure 
is  measured  by  the  product  of  the  mass  of  the  body  into  the 
velocity  which  would  be  generated  in  any  assumed  unit  of  time, 
as  one  second,  if  the  body  were  free  to  move  in  the  direction  in 
which  the  force  acts.  The  latter  factor  is  called  the  acceleration. 
In  the  case  of  the  atmosphere  the  force  is  that  of  gravity  acting 
in  a  direction  normal  to  the  earth's  surface ;  and  the  accelera- 
tion of  this  force,  usually  denoted  by  g,  at  the  sea-level  on  the 
parallel  of  45°,  if  the  unit  of  time  is  one  second,  is  9.8o6m  or 
32.17  feet.  The  atmosphere  being  subject  to  the  action  of  the 
force  of  gravity,  it  presses  upon  the  earth's  surface  at  any  given 
place  and  upon  itself  at  any  level  above  the  surface  very  nearly 
in  proportion  to  the  mass  of  air  above.  Since  the  force  of 
gravity  is  not  precisely  the  same  at  all  latitudes  and  altitudes, 
being  about  -^  part  greater  at  the  poles  than  at  the  equator, 
and  diminishing  a  little  with  increase  of  altitude,  the  same  mass 
of  air  does  not  press  with  quite  equal  force  at  all  latitudes  and 
altitudes. 

If  the  surface  upon  which  the  atmosphere  presses  is  that  of 
a  liquid,  and  any  part  of  it  is  entirely  relieved  of  this  pressure, 
as  in  the  case  of  a  barometer  tube  or  a  suction  pump,  the  liquid 
rises  until  the  pressure  of  the  vertical  column  is  exactly  equal 
to  that  of  a  column  of  atmosphere  of  the  same  base  extending 
up  to  its  top.  Since  the  volumes  of  different  liquids  are  inversely 


10    CONSTITUTION  AND  NA  TURE    OF    THE  A  TMOSPHERE. 

as  the  densities,  the  greater  the  density  the  less  in  proportion: 
is  the  volume,  and  consequently  the  height  to  which  the  liquid- 
has  to  ascend,  to  counterpoise  the  pressure  of  the  atmosphere. 

10.  For  any  given  standard  temperature,  as  that  of  melting 
ice,  the  height  of  the  liquid  column,  either  of  mercury  or  of 
water,  becomes  a  measure  of  the  atmospheric  pressure,  provided 
this  column  and  the  atmosphere  are  both  acted  upon  by  the  same 
intensity  of  the  force  of  gravity,  that  is,  force  per  unit  mass. 
This  latter  provision  becomes  necessary  as  well  as  that  of  equal- 
ity of  temperature,  since  the  pressure  is  measured  by  the  prod- 
uct of  the  mass  into  the  acceleration,  and  the  latter,  being  as 
the  intensity  of  force,  varies  slightly  with  a  change  of  both 
latitude  and  altitude.  A  true  measure  must  be  independent  of 
both  temperature  and  locality. 

Since  the  density  of  mercury  at  the  standard  temperature 
of  melting  ice  is  13.596  times  greater  than  that  of  water  at  the 
standard  temperature  of  4°  C,  which  is  that  of  its  maximum 
density,  the  column  of  water  has  to  rise  13.596  times  higher 
than  that  of  mercury,  both  being  taken  at  their  standard  tem- 
peratures, in  order  to  counterpoise  the  pressure  of  the  atmos- 
phere. Where  the  atmospheric  pressure,  as  it  usually  is,  is 
indicated  by  the  height  of  the  mercurial  column  as  observed  in 
the  barometer  tube,  it  is  called  the  barometric  pressure. 

When  the  height  of  the  mercurial  column  is  observed  under 
different  temperatures  and  subject  to  different  forces  of  gravity, 
there  must  be  a  reduction,  for  the  reason  just  given,  to  some 
standard  temperature  and  force.  The  assumed  standard  tem- 
perature is  that  of  melting  ice  or  zero  of  the  Centigrade  scale, 
and  the  reduction  to  this  standard  is  called  the  reduction  to 
freezing. 

Since  also  the  pressure  of  the  same  mass  of  mercury  is 
different  on  different  parallels  of  latitude,  and  at  different  alti- 
tudes, as  has  been  stated,  the  observations  of  the  barometer 
must  be  reduced  to  the  height  at  which  the  mercurial  column 
would  stand  if  placed  on  the  parallel  of  45°  and  at  sea-level. 
This  is  called  the  reduction  to  standard  gravity. 

The  average  barometric  pressure  for  all  seasons  and  for  all. 


PRESSURE   OF   THE  ATMOSPHERE.  II 

parts  of  the  earth's  surface  is  found  from  observation  to  be 
about  760  millimeters  (29.92  inches).  This  is  therefore  assumed 
as  the  pressure  of  an  atmosphere,  and  in  cases  of  very  great 
pressures  is  assumed  as  the  unit  of  pressure,  the  pressure  being- 
said  to  be  equal  to  a  certain  number  of  atmospheres.  It  is  also 
the  standard  pressure,  or  value  of  P0  in  §4,  in  giving  the  abso- 
lute and  relative  densities  of  gases. 

The  reductions  of  the  observed  heights  of  the  mercurial  col- 
umn at  sea-level,  which  may  be  assumed  to  be  sensibly  the 
reduction  of  76omm,  to  the  parallel  of  45°,  is  given  for  each 
degree  of  latitude  in  Table  I  of  the  Appendix.  For  the  par- 
allels from  o°  to  45°  the  reductions  are  negative  and  for  the 
rest  positive,  as  indicated  by  the  signs  placed  over  the  first  and 
last  columns  of  the  table. 

At  the  poles  the  pressure  of  the  mercurial  column  is  greater 
than  on  the  parallel  of  45°,  and  hence  the  height  at  which  it  must 
stand  in  order  to  counterpoise  the  pressure  of  the  atmosphere 
is  less  than  it  would  be  if  subject  to  the  standard  force  of 
gravity  of  the  parallel  of  45°,  and  so  it  must  be  increased  in 
order  to  reduce  it  to  this  standard.  At  the  equator  the  reverse 
is  true,  and  hence  the  reduction  there  is  negative.  Between 
the  parallels  of  45°  and  the  poles,  therefore,  the  reductions  are 
positive,  but  between  this  parallel  and  the  equator,  negative. 

For  pressures  at  different  altitudes  above  the  earth's  surface 
where  they  are  less  than  7o"omm  the  reductions  given  in  the  table 
must  be  decreased  in  proportion.  For  instance,  on  the  top  of 
Pike's  Peak  where  the  barometric  pressure  is  only  about  three 
fifths  of  that  at  the  sea-level,  the  proper  reduction  would  be 
only  about  three  fifths  of  that  given  in  the  table. 

The  forces  of  gravity  are  very  nearly  inversely  as  the 
squares  of  the  distances  from  the  earth's  surface.  Hence  at 
any  given  altitude  above  the  earth's  surface  the  pressure  of  the 
measuring  column  is  less  than  it  would  be  at  the  earth's  surface. 
There  must  be,  therefore,  a  negative  reduction  applied  for  the 
same  reason  as  there  is  at  the  equator,  where  the  pressure  of  the 
mercurial  column  is  less  than  it  is  on  the  parallel  of  45°.  This  re- 
duction in  millimeters  is  given  by  the  expression  —  0.000003  &P, 


12    CONSTITUTION  AND  NATURE    OF    THE  ATMOSPHERE. 

in  which  h  is  the  altitude  of  the  station  in  meters  and  P  the 
observed  barometric  pressure  in  millimeters.  The  exact  nu- 
merical coefficient  by  the  law  above  is  0.00000314,  but  this 
is  diminished  a  little  for  the  effect  of  the  increase  of  gravity  at 
the  top  by  the  attraction  of  the  mountain  mass.  This,  however, 
is  found  to  have  scarcely  any  sensible  influence.3  In  English 
inches  the  expression  above  is  —  0.0000232  kPt  in  which  h  must 
be  expressed  in  feet  and  P  in  inches.  The  reductions  for  any 
given  altitude  are  very  readily  obtained  from  these  simple 
expressions. 

11.  Since  force  or  pressure  is  measured  by  the  product  of 
the  mass  into  the  acceleration,  pressure  is  proportional  to,  and 
becomes  a  measure  of,  mass  where  the  acceleration  is  the  same 
for  both  the  measuring  and  the  measured  mass,  as  in  the  case 
of  ordinary  weighing,  by  counterpoising  the  one  against  the 
other,  both  having  the  same  position  upon  the  earth  with  regard 
to  latitude  and  altitude.  Two  masses  which  have  the  same 
pressures,  or,  in  other  words,  exactly  counterpoise  each  other 
where  they  are  suspended  at  equal  distances  from  the  fulcrum 
on  the  beam  of  the  balance,  are  said  to  have  the  same  weight. 
The  weight  of  a  body,  therefore,  is  proportional  to  the  mass, 
and  not  to  its  pressure  under  the  varying  positions  which  it  may 
have  with  regard  to  the  earth  and  other  attracting  bodies,  and 
is  therefore  a  measure  of  mass,  and  not  of  pressure. 

Any  mass  which  weighs  as  much  as  a  cubic  centimeter  of 
pure  water  at  the  standard  temperature  of  4°  C.,  which  is  that 
of  its  maximum  density,  is  called  a  gram.  But  if  this  is  used 
as  a  unit  of  pressure  instead  of  one  of  mass,  as  it  sometimes  is, 
this  unit  must  be  understood  to  be  the  pressure  of  a  gram  sub- 
ject to  the  standard  force  of  gravity  as  already  defined,  since 
the  pressure  of  the  same  mass  differs  in  different  localities. 
The  pressure  of  the  atmosphere  in  grams,  as  thus  defined,  on  a 
square  centimeter  of  the  earth's  surface  is  equal  to  the  height  in 
centimeters  of  a  column  of  pure  water  of  the  temperature  of 
4°  C.  and  subject  to  the  standard  force  of  gravity,  which  would 
exactly  counterpoise  it,  as  in  the  case  of  the  mercurial  column 
in  a  barometer ;  for  the  pressure  would  be  that  of  a  column  of 


PRESSURE   OF   THE  ATMOSPHERE.  1$ 

water  of  that  height  and  having  a  base  of  one  square  centimeter,, 
and  consequently  the  pressure  in  grams  would  be  equal  to  the 
number  of  centimeters  in  the  height  of  the  column.  Or,  since 
the  density  of  mercury  at  o°  C.  is  13.596  times  greater  than  that 
of  water  at  the  temperature  of  maximum  density,  it  is  equal 
to  the  height  in  centimeters  of  the  mercurial  column  in  the 
barometer  when  reduced  to  freezing  and  to  standard  gravity 
multiplied  into  13.596.  Hence  the  pressure  in  grams  of  a 
standard  atmosphere  of  a  barometric  pressure  of  760™™,  or 
76°™,  upon  each  square  centimeter  of  the  earth's  surface,  is 
76  X  13.596—1033.3.  This  upon  a  square  meter  is  10333  kilo- 
grams. 

As  a  centimeter  is  equal  to  0.3937  of  an  inch,  and  a  gram  is 
equal  to  0.00220462  of  a  pound  avoirdupois,  the  pressure  of 
such  an  atmosphere  in  pounds  avoirdupois  upon  a  square  inch 
is  1033.3  multiplied  into  0.00220462  and  divided  by  0.3937*, 
Avhich  gives  14.696. 

12.  The  density  of  air  relative  to  that  of  pure  water  of  the 
standard  temperature  of  4°  C.  is  called  its  absolute  density. 
But  as  air  is  very  elastic,  and  its  elasticity  depends  upon  both 
the  pressure  to  which  it  is  subject  and  its  temperature,  the 
density  is  a  very  indefinite  thing  unless  it  is  given  for  some 
standard  pressure  and  temperature.  The  density  of  pure  and 
dry  air  under  the  standard  barometric  pressure  of  76omm,  and 
standard  temperature  of  o°  C.,  deduced  from  Regnault's  experi- 
ments, is  0.00129278.  If  the  density  of  such  an  atmosphere 
were  the  same  at  all  altitudes  as  at  the  earth's  surface,  it  would 
of  course  have  a  definite  limit,  and  the  height  of  such  an  atmos- 
phere in  centimeters,  neglecting  the  very  slight  diminution  of 
gravity  with  increase  of  altitude,  would  be  1033. 3cm  divided  by 
0.00129278,  or  7993  meters;  for  1033. 3cm  is  the  height  of  a  column 
of  pure  water  at  the  temperature  of  4°  C.,  which,  being  subject 
to  the  action  of  the  force  of  standard  gravity,  counterpoises  a 
column  of  air  of  the  same  base  and  of  barometric  pressure  of 
76omm  which  extends  to  the  top  of  the  atmosphere ;  and  the 
height  of  a  column  of  air  of  uniform  density  must  be  to  that  of 
the  column  of  water  of  the  same  pressure  inversely  as  the 


14   CONSTITUTION  AND   NATURE  OF    THE   ATMOSPHERE. 

densities,  that  of  water  here  being  unity.  This  is  called  the 
.height  of  a  homogeneous  atmosphere. 

If  the  mass  of  the  atmosphere  were  increased  or  decreased 
in  any  given  ratio,  the  pressure  and  density  at  the  earth's  sur- 
face would  be  increased  or  decreased  in  precisely  the  same  ratio, 
and  consequently  the  height  of  the  corresponding  homogeneous 
atmosphere  would  in  all  cases  be  the  same.  This  may  also  be 
inferred  from  what  has  been  stated  in  §  8.  For  any  other 
temperatures  above  o°  C.  the  corresponding  heights  of  the 
homogeneous  atmospheres  would  be  -pfa  part  greater  for  each 
-degree  Centigrade  of  increase  of  temperature,  and  hence  for 
different  temperatures  they  would  be  as  the  absolute  temper- 
matures.  With  the  usual  amount  of  carbonic  acid  gas  in  the  air 
the  height  of  a  homogeneous  atmosphere  is  a  very  little  less 
than  in  the  case  of  a  pure  atmosphere  of  the  same  mass. 

In  hypothetical  atmospheres  of  the  different  kinds  of  gases 
it  is  evident  that  the  heights  of  the  corresponding  homogeneous 
atmospheres,  whatever  their  masses,  are  proportionally  greater 
for  gases  of  greater  than  for  those  of  less  elastic  force  ;  for  the 
<eflect  of  an  increase  of  elastic  force  is  the  same  whether  this 
arises  from  an  original  greater  velocity  imparted  to  the  molecules, 
or  from  an  increase  of  this  velocity  and  of  elasticity  by  means  of 
an  increase  of  temperature.  As  in  a  static  atmosphere  the  elastic 
force  and  pressure  are  equal  and  the  densities  for  different  kinds 
of  atmospheres  of  the  same  mass  are  inversely  as  the  elastic 
forces,  it  follows  that  the  heights  of  homogeneous  atmospheres 
of  different  elastic  forces  are  inversely  as  their  relative  densities. 
Hence  the  height  of  a  homogeneous  atmosphere  of  pure  and  dry 
air  being  7993  meters,  that  of  a  hydrogen  atmosphere  with  a 
relative  density  of  only  0.0692  would  be  7993/0.0692  =  115,506 
meters. 

13.  The  pressure  of  the  atmosphere  at  any  given  altitude 
can  be  computed  from  a  well-known  formula  where  the  tem- 
perature at  different  altitudes  is  known.  This,  for  the  aver- 
age conditions  of  the  atmosphere  for  all  places  and  at  all  alti- 
tudes, decreases  about  0.4°  C.  for  each  100  meters  of  increase 
of  altitude.  Assuming  that  it  decreases  at  this  rate,  and  that 


PRESSURE   OF    THE  ATMOSPHERE. 


the  temperature  at  the  earth's  surface  is  20°,  the  temperatures 
at  the  different  altitudes  given  in  the  second  column  of  the  fol- 
lowing table  will  be  those  of  the  first  column,  and  the  baro- 
metric pressures  at  the  several  altitudes  as  given  in  the  last 
column  : 


Temperatures 
°C. 

ALTITUDES  IN 

Pressures  in 
Millimeters. 

Kilometers. 

Miles. 

+  20 

0 

0.00 

760 

+  10 

2-5 

1.56 

565 

o 

5-o 

3." 

416 

—  IO 

7-5 

4.66 

301 

20 

IO.O 

6.21 

217 

30 

12.5 

7-77 

153 

40 

15.0 

9-32 

108 

50 

17.5 

10.87 

75 

60 

20.  o 

12.42 

5i 

80 

25.0 

15-53 

27 

100 

30.0 

18.63 

9 

I2O 

35-o 

21.74 

3 

-  140 

40.0 

24.85 

i 

The  pressures  are  computed  from  a  formula  based  upon 
^Boyle's  law,  which,  we  have  seen,  §  3,  may  not  hold  accurately 
up  to  the  altitude  of  40  kilometers,  where  the  atmosphere,  by 
this  law,  becomes  extremely  rare  ;  but  up  to  the  altitude  of  30 
kilometers,  and  higher,  the  deviations  from  the  law  are  ex- 
tremely small.  But  if  there  is  any  certain  evidence  that  the  at- 
mosphere extends  to  the  height  of  45  miles,  as  is  usually  said, 
and  with  a  density  sufficiently  great  to  indicate  its  existence 
there  by  means  of  reflected  light,  there  must  be  very  great 
deviations  from  this  law  at  low  pressures.  With  a  higher  tem- 
perature the  atmosphere  would  be  expanded  upward  more,  and 
consequently  the  pressures  would  not  decrease  so  rapidly  with 
increase  of  altitude  if  our  assumed  temperatures  in  the  upper 
part  of  the  atmosphere  in  the  preceding  table  were  greater,  but 
JIG  probable  error  in  these  assumed  temperatures  would  affect 
the  results  much  in  the  last  column  of  the  table. 

The  following  table  contains  a  few  of  the  observed  pressures 


1 6    CONSTITUTION  AND  NATURE    OF   THE  ATMOSPHERE. 

of  the  atmosphere  at  different  altitudes  in  different  parts  of  the 
earth : 


PLACES. 

ALTITUDES  IN 

Pressures  in 
Millimeters. 

Meters. 

Feet. 

Level  of  the  Ocean                                . 

0 
408 
1,200 
1,916 

2,479 
2,674 
3,320 
4.308 
6,100 
11,280 

O 

1,339 
3-937 
6,285 
8,130 

8,773 
10,893 

14,134 
20,014 
37,ooo 

760 
726 
660 
600 
565 
555 
5io 

45i 
360 
180 

Geneva  Observatory      ............ 

Summit  of  the  Great  St    Bernard  . 

The  Summit  of  the  Faulhorn  (Bravais)   

Pike's  Peak    

On  the  Chimborazo  (Humboldt  and  Bonpland). 
Glaisher's  highest  balloon  ascent 

These  pressures  are  annual  means  in  some  cases,  deduced 
from  a  series  of  years  of  observations,  but  mostly  they  have 
been  obtained  from  one,  or  at  most  only  a  few,  observations 
under  different  conditions  of  temperature  and  pressure  at  the 
surface,  and  some  of  the  altitudes  were  only  approximately 
known. 

Table  VI,  Appendix,  contains  the  height,  in  meters,  of  a 
column  of  dry  air,  corresponding  to  a  millimeter  of  the  barome- 
ter at  different  temperatures  and  under  different  barometric 
pressures.  This  will  be  found  useful  in  the  course  of  this  work, 
and  is  of  great  practical  value  for  various  purposes.  For  in- 
stance, in  balloon  ascents  and  in  the  ascent  of  high  mountains, 
with  the  observed  barometric  pressure  and  temperature  as  ar- 
guments, the  table  indicates  the  amount  of  ascent  or  descent 
corresponding  to  each  change  of  one  millimeter  in  the  baro- 
metric pressure. 

AQUEOUS  VAPOR  OF  THE  ATMOSPHERE. 

14.  If  the  atmosphere  had  the  same  temperature  at  all  alti- 
tudes, and  were  in  a  perfectly  quiet  state,  the  aqueous  vapor 
contained  in  it  would  form  an  independent  atmosphere  around 
the  globe  of  the  same  nature  as  that  of  oxygen  or  nitrogen,  §  6, 
and  it  would  be  distributed  through  the  other  elements  in  ac- 


AQUEOUS   VAPOR   OF   THE  ATMOSPHERE.  I/ 

cordance  with  Dalton's  law,  and  so  it  wrould  exist  at  all  altitudes 
in  the  same  proportions  as  if  the  dry  atmosphere  were  not  pres- 
ent, and  the  densities  would  be  such  as  are  given  by  the  laws 
of  Boyle  and  of  Charles,  just  as  in  the  case  of  the  other  gases.* 
But  on  account  of  its  less  relative  density  than  that  of  the  at- 
mosphere, 0.622,  it  would  be  expanded  upward  more,  so  that  it 
would  be  necessary  to  ascend  higher  than  in  the  atmosphere,  in 
the  ratio  of  I  to  0.622,  before  getting  above  the  half  or  any 
other  proportion  of  it,  and  it  would  exist  in  greater  proportions 
in  comparison  with  the  other  constituents,  oxygen  and  nitrogen, 
in  the  higher  altitudes  than  at  and  near  the  earth's  surface.  But 
it  so  happens  that  the  prevailing  temperatures  of  the  atmos- 
phere are  those  at  which  aqueous  vapor  of  considerable  ten- 
sion is  condensed  into  liquid,  and  as  the  temperature  decreases 
with  increase  of  altitude,  the  vapor  tension  at  the  different  al- 
titudes is  not  determined,  as  in  the  case  of  the  other  constitu- 
ents of  the  atmosphere,  by  the  laws  of  Boyle  and  of  Charles,  but 
by  the  temperatures  alone  which  exist  at  these  altitudes,  and 
hence  by  a  law  which  is  very  different.  It  is  found  from  ex- 
periment that  to  any  given  temperature  there  corresponds  a 
certain  maximum  vapor  tension,  which  is  the  same  whether  the 
vapor  exists  alone  or  forms  a  constituent  of  the  atmosphere, 
and  if  by  any  means  the  tension  is  increased  above  this,  a  part 
of  the  vapor  is  at  once  condensed  and  the  tension  reduced  to 
the  maximum  corresponding  to  the  existing  temperature. 

15.  The  maximum  vapor  tensions  corresponding  to  the  given 
temperatures,  which  include  mostly  those  within  the  range  of 
ordinary  observation,  are  given  in  Table  II.  They  have  been 
deduced  from  Regnault's  experiments  by  the  International  Bu- 
reau of  Weights  and  Measures.  The  table  will  be  convenient 
for  reference  in  studying  the  relations  between  the  vapor 
tension  and  the  temperature,  and  the  relations  between  the  ab- 
solute maximum  tension  which  can  exist  in  the  air  at  any  given 
altitude  and  temperature  and  that  which  could  exist  by  the  laws 
of  Boyle  and  of  Charles. 

If  the  temperature  at  the  earth's  surface  were  25°, 
and  the  same  at  all  altitudes,  and  the  vapor  tension  2 


1 8    CONSTITUTION  AND  NATURE   OF  THE  ATMOSPHERE. 

then,  in  a  quiet  state  of  the  atmosphere,  its  distribution 
with  regard  to  altitude  would  be  according  to  Dalton's 
law,  or  such  as  would  take  place  if  the  vapor  were  an  in- 
dependent atmosphere,  in  accordance  with  the  laws  of  Boyle 
and  of  Charles.  But  since  the  temperature  of  the  atmosphere 
decreases  usually  with  increase  of  altitude,  and  at  such  a 
rate  that  the  maximum  tension  corresponding  to  it  decreases 
more  rapidly  than  it  would  by  the  laws  of  Boyle  and  of  Charles, 
the  maximum  tension  is  that  of  Table  II  corresponding  to  the 
existing  temperature,  and  is  usually  less  than  what  would  be 
given  by  Dalton's  law.  It  is  seen  from  the  table  that  at  any  al- 
titude where  the  temperature  is  at  the  zero  of  the  Centigrade 
scale  the  maximum  vapor  tension  which  can  exist  there  is  only 
4.569mm  ;  whatever  may  be  the  tension  at  and  near  the  earth's 
surface,  where  a  warmer  temperature  prevails.  By  the  laws  of 
Boyle  and  of  Charles,  if  the  vapor  tension  were  2Omm  at  the 
earth's  surface,  at  the  altitude  of  5  kilometers  (3.1  miles)  it 
would  be  about  i3mm ;  but  if  at  that  altitude  there  was  the  tem- 
perature of  o°  C.,  it  is  seen  from  the  table  that  the  maximum 
tension  which  could  exist  there  would  be  only  about  one  third 
of  that. 

As  the  vapor  rises  or  is  diffused  upward  to  altitudes  where 
the  temperature  is  less  than  that  which,  by  the  table,  corre- 
sponds to  its  tension,  the  vapor  is  condensed  and  the  tension 
reduced  to  the  maximum  corresponding  to  the  temperature  as 
determined  by  the  table.  When  the  air  contains  as  much  vapor 
as,  at  the  given  temperature,  can  exist  in  it,  it  is  said  to  be  sat- 
urated,  and  the  temperature  of  unsaturated  air  at  which,  as  it 
cools,  the  vapor  begins  to  condense  is  called  the  dew-point. 
Where  the  vapor  tension  of  the  atmosphere  is  known  from  hy- 
grometrical  observations  of  any  kind,  this  point  is  readily  de- 
termined from  Table  II,  it  being  the  temperature  in  the  first 
column  to  which  corresponds  the  observed  tension  ;  for  at  this 
temperature  the  air  is  saturated,  and  if  it  cools  still  lower,  con- 
densation takes  place.  For  instance,  if  the  observed  vapor  ten- 
sion is  I7.363mm,  then  the  air,  whatever  its  initial  temperature, 
has  to  cool  down  to  20°  C.  before  condensation  takes  place,  and 


AQUEOUS    VAPOR   OF   THE  ATMOSPHERE.  1 9 

this  is  the  dew-point  belonging  to  this  assumed  hygrometric  state 
of  the  atmosphere. 

The  observed  vapor  tension  of  the  atmosphere  in  comparison 
with  the  tension  of  saturation  at  the  observed  temperature  is 
called  the  relative  humidity.  For  instance,  if,  in  the  example 
above,  the  temperature  of  the  air  were  30°  C.,  then  the  tension  of 
saturation,  by  the  table,  would  be  3i.5imm,  and  hence  the  relative 
humidity  equal  17.363  :  31.51  =  0.55,  or  55  per  cent. 

16.  The  amount  of  aqueous  vapor  in  the  atmosphere  is  very 
variable,  both  at  different  places  on  the  earth's  surface  and  at  dif- 
ferent altitudes,  at  the  same  time,  and  in  the  same  locality  at  dif- 
ferent times.  The  mere  diffusion  of  aqueous  vapor  through 
the  atmosphere,  as  that  of  any  one  gas  through  another,  takes 
place  slowly ;  so  that,  as  the  water  of  the  ocean  and  of  moist  land 
surfaces  is  evaporated,  it  penetrates  through  the  lower  strata  of 
the  air  very  slowly,  and  remains  mostly  near  the  earth's  surface, 
unless  there  is  an  ascending  current  to  carry  it  upward,  and  when 
the  air  is  calm  it  may  be  nearly  or  quite  saturated  at  the  earth's 
surface,  while  it  is  comparatively  dry  at  only  small  altitudes 
above  it.  On  account  also  of  the  slow  rate  of  diffusion,  and  the 
absence,  often,  of  rapid  convective  currents,  the  vapor  generally 
abounds  more  over  water  surfaces  and  damp  places,  and  less 
over  the  interior  and  dry  parts  of  the  continents.  Since,  also, 
the  temperature  of  the  air  is  almost  always  much  less  in  the 
upper  than  the  lower  strata  of  the  atmosphere,  the  absolute 
amount  of  vapor  which  can  exist  in  the  upper  strata,  as  we 
have  seen  in  §  14,  is  small  even  when  the  air  is  completely  sat- 
urated, and  it  generally  falls  much  belo\^  this.  For  the  same 
reason  the  amount  of  vapor  in  high  polar  latitudes,  where  the 
temperature  is  generally  very  low,  is  small  in  comparison  with 
that  in  the  lower  and  much  warmer  latitudes.  The  aqueous 
vapor  is,  therefore,  very  irregularly  distributed,  in  general,  both 
with  regard  to  the  earth's  surface  and  also  altitude,  and  not  at  all 
as  it  would  be  as  an  independent  atmosphere  existing  alone,  or  as 
it  would  in  a  quiet  atmosphere  in  \vhich  it  would  have  time  to 
be  equally  diffused  laterally  to  all  places,  and  upward,  so  as 
to  satisfy  Dalton's  law,  in  case  the  temperature  at  all  places 


20   CONSTITUTION  AND  NA  TURE   OF   THE    A  TMOSPHERE. 

and  altitudes  were  so  great  that  no  condensation  would  take 
place. 

Since  the  temperature  of  the  atmosphere  is  very  change- 
able, and  the  absolute  amount  of  vapor  which  can  exist  in  it, 
by  the  table,  depends  very  much  upon  the  temperature,  the 
actual  amount  found  in  it  must  also  be  very  different  at  differ- 
ent times  in  the  same  locality,  so  that  it  is  very  variable  both 
with  regard  to  space  and  time. 

DYNAMICAL  HEATING   AND   COOLING   OF  THE  AIR. 

17.  It  is  well  known  that  if  air  or  any  gas  is  suddenly  com- 
pressed there  is  an  increase  of  its  temperature,  and  the  contrary 
if  the  pressure  is  removed  and  it  is  allowed  to  suddenly  expand. 
The  former  is  seen  in  the  sudden  compression  of  air  in  a  con- 
densing syringe  or  in  a  pneumatic  tinder-box,  in  which  light 
and  dry  substances  may  be  ignited  from  the  increased  tempera- 
ture, and  the  latter,  in  the  rarefaction  of  air  in  the  receiver  of 
an  air-pump,  by  which  it  is  soon  so  cooled  that  the  aqueous 
vapor  contained  in  it  is  condensed. 

The  action  of  a  force  F  through  the  space  s  is  called  work. 
If  the  force  is  constant  through  the  whole  space,  the  product, 
Fs,  of  the  force  into  the  space  is  the  measure  of  the  work. 
Where  the  force  varies,  the  amount  of  work  can  only  be  ob- 
tained by  integrating  the  products  of  each  element  of  the 
spaces  into  the  force  corresponding  to  it.  Work  usually  con- 
sists in  moving  bodies  in  opposition  to  the  force  of  gravity,  or 
in  overcoming  inertfa  in  the  case  of  the  acceleration  of  the 
motions  of  bodies,  or  in  overcoming  frictional  or  other  resist- 
ances to  motion,  by  the  application  of  some  force. 

If  a  body  is  raised  vertically  through  the  space  s  by  the 
application  of  any  kind  of  force,  a  certain  amount  of  work  has 
been  done  to  place  it  in  this  position.  The  force  which  has 
been  overcome  is  the  force  of  gravity,  equal  gm,  where  ^rep- 
resents the  acceleration  of  the  force  of  gravity  and  m  the  mass 
of  the  body.  The  force  applied  is  equal  to  that  overcome,  and. 
so  the  amount  of  work  done  is  gsm. 


DYNAMICAL  HEATING  AND   COOLING   OF   THE  AIR.      21 

18.  The  capacity  for  doing  work  is  called  energy.  The 
elevated  body  now,  acted  upon  by  the  force  of  gravity,  if  it  has 
.space  to  move  through,  has  the  power  of  overcoming  inertia, 
•or  resistance  of  any  kind  to  its  motion.  It  consequently  has 
•energy,  and  this  is  usually  called  potential  energy,  sometimes 
.energy  of  position,  and  is  exactly  equal  to  the  amount  of  energy 
spent,  of  whatever  kind,  in  raising  it  to  its  position.  If  the 
body  in  falling  is  not  obstructed  in  its  motion  by  some  resist- 
ing medium  or  frictional  resistance,  this  potential  energy  is  all 
:spent  in  overcoming  the  inertia  of  the  body  in  producing  ac- 
celerated motion.  Letting  v  represent  the  velocity  of  motion 
corresponding  to  the  space  s  passed  over,  we  have  by  the  well- 
known  relations  between  the  space  and  velocity  in  the  case  of 
falling  bodies,  gs  =  \v*,  and  so  the  amount  of  energy  spent  in 
producing  this  velocity  or  the  momentum  mv,  is  gsm  =  \v*m. 
But  this  body  in  motion  now  has  the  capacity  of  overcoming 
other  forces  or  resistances,  and  consequently  has  energy,  called 
.kinetic  energy,  formerly  vis  viva  or  living  force,  and  the  meas- 
ure of  this  energy  is  equal  to  that  of  the  work  gsm  spent  in 
producing  it,  and  consequently  equal  to  ^m.  The  kinetic 
energy  is  therefore  proportional  to  the  square  of  the  velocity. 

It  is  well  known  that  heat  is  produced  by  the  concussion  of 
inelastic  bodies.  If  the  body,  of  mass  in,  after  having  acquired 
in  any  way  the  velocity  v,  should  be  brought  to  rest  by  contact 
with  another  body,  as  in  the  case  of  completely  inelastic  bodies, 
it  would  then  have  lost  all  of  its  kinetic  energy.  This  kind  of 
•energy  is  thus  transformed  into  heat,  which  is  a  well-known 
agent  in  doing  many  kinds  of  work,  and  is  called  thermal  energy. 
If  the  velocity  v  is  produced  by  potential  energy,  then  this  is 
directly  transformed  into  kinetic  energy,  and  thus  indirectly 
into  thermal  energy. 

If  a  falling  body  or  a  body  descending  in  any  way  from  a 
higher  to  a  lower  level,  is  retarded  by  the  action  of  a  resisting 
medium  or  by  friction,  then  the  potential  energy  is  spent  par- 
tially in  giving  momentum  or  kinetic  energy  to  the  body  and 
to  certain  parts  of  the  fluid,  and  partly  in  causing  heat.  But 
as  soon  as  the  body  is  brought  to  rest,  and  likewise  all  parts  of 


22    CONSTITUTION  AND   NATURE   OF   THE  ATMOSPHERE. 

the  fluid  in  the  case  of  a  resisting  medium,  then  all  the  kinetic, 
energy  generated  at  first,  is  likewise  transformed  into  heat,  and 
the  whole  amount  is  proportional  to  the  amount  of  potential 
energy  of  the  body  spent  in  descending  to  a  lower  level.  This 
heat  is  contained  partly  in  the  body  acted  upon,  and  partly  in 
the  resisting  medium  or  body  offering  the  frictional  resistance. 

19.  We  have  seen  that  a  given  amount  of  potential  energy 
can  be  transformed  into  a  corresponding  amount  of  kinetic 
energy.  Conversely,  this  kinetic  energy  can  be  transformed 
back  again  into  potential  energy,  as,  for  instance,  where  the 
whole  momentum  acquired  is  used  up  in  causing  the  body  to 
ascend  against  the  force  of  gravity,  in  which  case  the  body  as- 
cends exactly  to  the  height  from  which  it  had  fallen  in  generat- 
ing the  kinetic  energy,  and  so  the  same  amount  of  potential 
energy  is  reproduced  which  was  spent  in  producing  the  kinetic 
energy.  But  there  must  not  be  any  resisting  medium  or  fric- 
tional resistance  affecting  either  the  descending  or  ascending^ 
motion  of  the  body.  In  like  manner  the  heat  generated  by  a 
given  amount  of  kinetic  energy  can  be  used  to  reproduce  this 
energy,  and  if  it  could  be  applied  without  loss  it  would  give 
rise  to  exactly  the  same  amount  of  kinetic  energy  as  was  spent 
in  producing  it.  Hence  each  of  these  three  kinds  of  energy 
can  be  transformed,  either  directly  or  indirectly,  into  each  of 
the  others;  and  the  amount  of  energy  in  each  case,  if  it  could 
be  applied  in  doing  work  without  loss,  would  do  the  same 
amount  of  work.  The  same  is  true  with  regard  to  other  kinds 
of  energy  which  might  be  named.  In  fact,  work  is  simply  the 
creation  of  energy  of  some  kind  at  the  expense  of  another,  or 
the  transformation  of  one  kind  of  energy  into  another.  In  this 
way,  at  the  expense  of  either  heat  or  kinetic  energy,  the  work  of 
raising  a  body  against  the  force  of  gravity  is  performed,  or,  in 
other  words,  potential  energy  is  produced.  The  same,  in  doing 
the  work  of  overcoming  frictional  resistances  to  motion,  gener- 
ates as  much  heat  as  is  spent,  though  it  may  be  so  scattered  as. 
not  to  be  perceptible. 

In  the  compression  of  air  a  certain  amount  of  work  is  done 
at  the  expense  of  some  kind  of  energy.  This  is  transformed 


DYNAMICAL   HEATING  AN.D   COOLING   OF   THE  AIR.      2$ 

for  the  most  part  directly  into  heat,  the  amount  of  kinetic 
energy  in  the  motion  of  the  air  in  being  compressed,  and  which 
is  transformed  into  heat  energy  as  soon  as  all  motion  ceases, 
being  very  small.  If  heat  energy  were  the  agent  used  in  the 
compression,  and  it  could  be  applied  without  loss,  the  heat  of 
the  compressed  air  would  be  increased  by  the  amount  of  heat 
expended  in  the  compression.  The  whole  amount  of  energy, 
therefore,  remains  the  same,  and  is  not  diminished  in  doing 
work.  This  principle  is  called  the  conservation  of  energy. 

20.  If  the  whole  potential  energy  of  a  raised  body,  subject 
to  the  action  of  the  force  of  gravity,  is  spent  in  falling,  by 
means   of  some  mechanical  contrivance,  in  agitating  a  given 
amount  of  water,  and  so  heating  it  by  means  of  friction,  the 
amount  of  heat  generated  is  the  equivalent  of  the  potential  en- 
ergy spent,  and  so  of  the  work  required  to  raise  the  body.     In 
this  way  we  can  compare  the  work  with  the  heat  produced  by 
its  equivalent  potential  energy,  and  hence  get  an  equivalent  ex- 
pression of  one  in  terms  of  the  other,  whatever  the  units  used 
in  the  measure  of  each.     The  raising  of  one  kilogram,  subject 
to  the  force  of  standard  gravity,  through  one  meter,  called  a 
kilogram-meter,  is  taken  as  the  unit  of  work.     The  unit  of  heat 
is  the  amount  of  heat  required  to  raise  the  temperature  of  a 
unit  mass  of  pure  water  from  o°  to  i°  C.     The  unit  of  water 
which  is  usually  assumed  in  the  unit  of  work  is  the  kilogram, 
and  so  the  heat  unit  in  this  case  is  the  amount  of  heat  required 
to  raise  the  temperature  of  a  kilogram  of  pure  water  from  o° 
to    i°  C.      According   to    the  most   recent  experiments,4  the 
height  to  which  a  unit  of  heat  is  capable  of  raising  one  kilo- 
gram, subject  to  the  force  of  standard  gravity,  may  be  put  at 
430  meters,  the  equivalent  of  which  would  be  the  raising  of  430 
kilograms  through  one  meter.     Hence  the  capacity  of  such  a 
heat  unit  for  doing  work  is  430  kilogram-meters.     This  is  called 
the  mechanical  equivalent  of  heat.     The  amount  of  heat,  there- 
fore, required  to  do  one  unit  of  work,  called  the  equivalent  oj 
work,  is  the  reciprocal  of  this  number,  or  -£%-$  of  a   unit  of 
heat. 

21.  If  heat  is  applied  to  any  given  portion  of  air  which  is 


24   CONSTITUTION  AND  NATURE   OF   THE  ATMOSPHERE. 

free  to  expand,  a  part  of  this  heat  is  consumed  in  the  work  of 
expansion  and  the  balance  only  goes  toward  heating  the  air. 
Taking  a  simple  case,  if  we  have  a  cubic  meter  of  pure  and  dry 
air  at  the  standard  temperature  of  o°  C,  and  under  the  stan- 
dard pressure  of  one  atmosphere,  and  free  to  expand  in  one 
direction  only,  the  heat  which  raises  this  cubic  meter  of  air 
through  one  degree  of  temperature,  we  have  seen  in  §  4,  ex- 
pands it  in  this  one  direction  -^^  part  of  one  meter.  The  resist- 
ance to  the  expansive  force  in  the  expansion  is  the  pressure  of 
a  standard  atmosphere  on  a  square  meter  of  surface,  which  is 
10,333  kilograms  (§  n).  The  space  through  which  this  resist- 
ance is  overcome  being  ^¥  of  a  meter,  the  amount  of  work 
done  in  the  expansion  in  kilogram-meters  is  10333  X  -%%-%  = 

37-85- 

If  the  cubic  meter  of  air  should  expand  equally  in  each  of 
the  directions  normal  to  its  six  surfaces,  then  the  space  through 
which  each  surface  of  the  cube  would  move,  for  the  same  ex- 
pansion of  volume,  would  be  only  \  as  much,  but  the  amount  of 
surface  moved  and  force  overcome  would  be  six  times  as  much, 
and  so  the  amount  of  work  done  would  be  precisely  the  same. 
Moreover,  whatever  may  be  the  figure  of  the  volume  of  air 
equal  to  that  of  one  cubic  meter,  and  the  amount  of  surface, 
and  the  amount  of  displacement  of  this  surface  in  the  various 
directions  perpendicular  to  the  surface,  the  same  amount  of 
work  is  done  in  the  same  expansion  of  volume  ;  for  the  work 
done  is  proportional  to  the  sum  of  all  the  elements  of  surface 
multiplied  into  the  space  through  which  they  move  in  the  ex- 
pansion, and  the  pressure  or  resisting  force  being  the  same  on 
all  sides,  the  amount  of  work  done  is  the  same  in  all  cases  for 
the  same  expansion  of  volume. 

22.  The  same  masses  of  different  bodies  at  the  same  tem- 
perature require  different  amounts  of  heat  to  raise  their  temper- 
atures through  one  degree.  By  the  definition  of  a  heat  unit, 
§  20,  it  requires  one  unit  of  heat  to  raise  the  temperature  of  a 
kilogram  of  pure  water  from  o°  to  i°  C. ;  but  it  is  found  from 
experiment  that  to  raise  the  temperature  of  a  kilogram  of  pure 
and  dry  air,  under  constant  pressure,  from  o°  to  i°  C.,  only 


DYNAMICAL  HEATING  AND   COOLING   OF   THE  AIR.      2$ 

0.2375  of  a  unit  of  heat  is  required.  This  is  called  the  specific 
heat  of  air. 

According  to  the  results  obtained  by  the  International  Bu- 
reau of  Weights  and  Measures  from  the  experiments  of  Reg- 
nault,  a  cubic  meter  of  pure  dry  air  of  standard  pressure  and 
temperature  weighs  1.29278  kilograms.  Multiplying  this  into 
the  specific  heat  of  air,  we  get  1.29278  X  0.2375  =  0.30703  of  a 
heat  unit  as  the  amount  required  to  increase  the  temperature  of 
the  air  by  one  degree,  and  so  to  expand  the  cubic  meter  of  air 
^ o_  part  of  its  volume,  since  it  expands  so  much  for  each  degree 
of  increase  of  temperature.  But  we  have  just  seen  that  in  this 
expansion  the  amount  of  work  done  is  37.85  kilogram-meters. 
Dividing  this  therefore  by  0.30703,  we  get  123.28  kilogram- 
Tneters  as  the  amount  of  work  done  by  a  unit  of  heat  in  expand- 
ing the  cubic  meter  of  air  the  ^fg-  part  of  its  volume. 

If  the  cubic  meter  of  air,  of  whatever  figure,  were  subject 
to  any  other  than  the  standard  barometric  pressure  of  76omm, 
then  the  work  corresponding  to  any  given  amount  of  expan- 
sion of  the  volume  would  be  in  proportion  to  the  pressure,  and 
consequently  to  the  density,  where  the  temperature  is  constant. 
But  the  amount  of  heat  required  to  raise  the  temperature  of  a 
given  volume  of  air  through  one  degree  is  likewise  in  proportion 
to  the  density.  Hence  the  same  amount  of  heat  is  required  to 
be  applied  to  the  cubic  meter  of  air  to  do  a  certain  amount  of 
work  of  expansion,  whatever  the  pressure  and  density  may  be. 

Where  the  cubic  meter  of  air  has  temperatures  differing  from 
that  of  o°,  the  amounts  of  expansion,  and  consequently  of 
work  done,  by  the  heat  which  raises  its  temperature  by  a  given 
quantity,  are  inversely  as  the  absolute  temperatures,  being  a 
constant  part  of  the  volume  when  reduced  to  the  temperature 
of  o°.  But  the  amounts  of  heating  by  a  given  quantity  of  heat 
are  directly  as  the  absolute  temperatures,  being  inversely  as  the 
densities.  The  same  quantity  of  heat,  therefore,  applied  to  the 
cubic  meter  of  air  at  all  temperatures  does  the  same  work  of 
expansion. 

Again,  if  a  unit  or  any  other  quantity  of  heat  is  applied  to 
any  other  volume  than  a  cubic  meter  under  the  same  circum- 


26    CONSTITUTION  AND  NATURE   OF   THE  ATMOSPHERE. 

stances,  there  is  the  same  work  of  expansion  done,  for  the 
greater  the  volume,  of  whatever  figure,  the  greater  the  surface, 
but  the  less  in  proportion  is  the  heating  and  the  space  through 
which  this  surface  is  moved,  by  the  application  of  the  same 
amount  of  heat. 

From  what  has  been  shown,  it  now  follows  that  the  amount 
of  work  of  expansion  done  by  a  given  quantity  of  heat  is  the 
same  whatever  the  pressure,  temperature,  and  volume  may  be 
to  which  it  is  applied,  and  in  all  cases  the  amount  of  work  done 
by  a  unit  of  heat  is  123.28  kilogram-meters.  But  the  whole 
work  equivalent  of  this  heat  unit  is  430  kilogram-meters,  and 
therefore  the  part  of  the  heat  used  in  doing  the  work  of  expan- 
sion is  to  the  whole  as  123.28  to  430,  or  as  0.2867  to  unity.  Of 
a  unit  of  heat,  therefore,  applied  to  any  given  volume  of  air,. 
0.2867  of  a  unit  is  used  in  doing  work,  and  the  balance,  0.7133 
of  a  unit,  goes  toward  heating  the  air. 

23.  Where  the  air  is  not  allowed  to  expand  there  is  no  work 
done  at  the  expense  of  the  heat  supplied,  and  the  whole  goes 
toward  heating  the  air.     The  increase  of  temperature,  there- 
fore, given  to  air  by  a  certain  amount  of  heat  communicated  to 
it  where  it  is  not  allowed  to  expand,  is  to  that  in  the  case  of 
expansion   under  constant  pressure  in   the   ratio   of    unity  to 
0.7133,  or  as  1.402  to  unity.      Conversely,  the  heat  required  to 
raise  the  temperature  of  a  given  quantity  of  air  through  one 
degree  under  constant  volume  is  to  that  required  in  the  case  of 
expansion  under  constant  pressure  as  unity  to   1.402.      The 
specific  heat  of  air,  therefore,  under  the  latter  conditions  being 
0.2375,  in  the  case    of  constant  volume  it  is  0.2375/1.402  = 
0.1694. 

We  have  seen  that  of  the  heat  communicated  to  air  under 
constant  pressure  which  raises  its  temperature  one  degree,  the 
part  0.2867  is  used  in  doing  the  work  of  expansion.  Conse- 
quently, if  no  heat  is  communicated,  and  the  same  work  of 
expansion  is  done  in  the  air's  coming  under  different  pressures, 
this  work  is  done  at  the  expense  of  the  heat  already  in  the  air, 
and  hence  it  is  cooled  o°.2867  by  this  expansion. 

24.  In  order  to  obtain  the  heating  effect  of  compression,  or 


DYNAMICAL  HEATING  AND   COOLING   OF   THE  AIR.      2JT 

the  cooling  effect  of  expansion,  we  must  compute  the  amount 
of  work  spent  in  compression,  or  of  work  done  in  expansion, 
and  then  the  equivalent  of  this  work  in  heat  units  is  equal  to 
the  number  of  kilogram-meters  of  work  divided  by  430.  Each 
one  of  these  heat  units  produced  by  the  expenditure  of  work 
in  compression  would  raise  the  temperature  of  a  kilogram  of 
water  one  degree,  but  as  the  specific  heat  of  air  under  constant 
volume,  in  which  case  no  heat  is  spent  in  doing  work,  is  0.1694, 
the  temperature  of  a  kilogram  of  air  would  be  raised  in  the 
ratio  of  unity  to  0.1694,  or  to  5°.9  by  each  unit  of  heat  pro- 
duced by  the  work  of  compression.  Each  unit  of  work,  there- 
fore, would  heat  a  kilogram  of  air  the  -^  of  5°.9,  or  o°.oi37. 
On  the  contrary,  for  each  unit  of  work  done  in  expansion  at  the: 
expense  of  the  heat  in  a  kilogram  of  air,  it  is  cooled  by  the 
same  amount. 

In  the  compression  or  expansion  of  confined  air  the  work 
expended  in  the  one  case,  or  done  in  the  other,  is  not  propor- 
tional to  the  amount  of  contraction  or  expansion  of  the  volume, 
since  the  force,  or  resistance  overcome,  is  constantly  changing, 
becoming  continually  greater  in  case  of  compression,  and  less 
in  that  of  expansion,  so  that  the  amount  of  work  can  be  com- 
puted accurately  only  by  means  of  a  logarithmic  formula. 
Under  the  special  case,  however,  where  heat  is  communicated 
to,  or  taken  away  from,  air  under  constant  pressure,  the  force 
is  constant,  and  the  work  done  in  the  expansion,  or  spent  in 
compression,  is  proportional  to  the  change  of  volume. 

25.  We  now  come  to  the  subject  of  the  cooling  or  heating^ 
of  air  in  ascending  or  descending  currents.  The  amount  of 
expansion  of  air  under  constant  pressure  corresponding  to  an 
increase  of  temperature  of  i°  is  ^±-$  of  the  volume  at  the  tem- 
perature of  o°  C.  Hence  wehn  the  volume  of  air  in  coming 
under  less  pressure  expands  so  rapidly  that  there  is  no  time  for 
it  to  gain  or  lose  heat  by  radiation  or  conduction,  it  loses  o°.2867 
of  temperature  for  each  expansion  of  ^iy  of  its  volume  at  the 
temperature  of  o°  C.,  and  consequently  this  expansion  must  be 
increased  in  the  ratio  of  unity  to  0.2867,  or  to  y^Vy  part  of  its: 
volume  in  order  to  cool  one  degree. 


28    CONSTITUTION  AND  NA  TURE   OF    THE  A  TMOSPHERE. 

It  has  been  shown,  §  n,  that  the  height  of  a  homogeneous 
atmosphere,  at  the  temperature  of  o°  C.,  reckoned  from  the 
earth's  surface  or  any  other  level,  is  7993  meters.  If,  therefore, 
air  of  this  temperature  ascends  one  meter,  the  pressure  is 
diminished,  and  the  volume  increased,  the  T-^-  part.  Hence, 
dividing  ^g^y  by  T-^V3>  we  get  102.1  meters  for  the  height  to 
which  the  air  must  ascend  to  cool  one  degree.  This  gives  a 
rate  of  cooling  of  air  in  its  ascent  of  o°.98  very  nearly  for  each 
100  meters  of  ascent. 

For  other  temperatures  than  that  of  o°  C.,  the  masses  of 
air  left  below  in  ascending  one  meter,  and  consequently  the 
diminutions  of  pressure,  are  inversely  as  the  absolute  tem- 
peratures, and  consequently  the  amounts  of  expansion  of 
volume  at  those  temperatures  are  in  the  same  proportion.  But 
the  volumes  for  different  temperatures  are  directly  as  the  abso- 
lute temperatures.  The  air  therefore  in  ascending  one  meter, 
whatever  its  temperature,  is  expanded  the  Y^g-¥  part  of  its 
volume  at  the  temperature  of  o°  C.,  and  hence  is  cooled  by  the 
same  amount  as  in  the  case  of  air  of  the  temperature  of  o°  C. 
For  all  temperatures  of  the  air,  therefore,  it  has  to  ascend 
through  102.1  meters  to  cool  i°,  and  hence  cools  o°.98  for  each 
100  meters  of  ascent. 

In  the  case  of  air  descending  vertically  we  have  compression 
instead  of  expansion,  and  consequently  a  heating  instead  of  a 
cooling,  and  at  the  same  rate.  Since  the  cooling  in  the  one 
case  depends  upon  expansion,  and  the  heating  in  the  other 
upon  compression,  it  is  not  necessary  that  the  ascent  or  descent 
should  be  vertical,  but  only  that  the  air  should  come  under  dif- 
ferent pressures,  and  consequently  arrive  at  different  levels,  and 
the  rate  of  cooling  or  heating  is  o°.98  for  each  100  meters  of 
change  of  level,  whatever  be  the  directions  of  ascent  or 
descent. 

26.  Where  the  ascending  air  is  saturated  with  aqueous 
vapor,  the  cooling  arising  from  the  expansion  continually 
diminishes  the  capacity  of  the  air  for  moisture,  for  by  Table  II 
the  lower  the  temperature  the  less  the  amount  of  vapor  which 
•  can  exist  in  the  air.  Hence,  as  the  saturated  air  ascends  and 


DYNAMICAL  HEATING  AND   COOLING  OF  THE  AIR.     2$ 

cools,  the  aqueous  vapor  is  condensed,  and  the  latent  heat 
gradually  given  out,  as  condensation  takes  place,  raises  the  tem- 
perature of  the  air  above  what  it  would  otherwise  be,  and  thus 
causes  the  rate  of  cooling  of  the  ascending  saturated  air  to  be 
much  less  than  in  the  case  of  dry  or  unsaturated  air. 

The  number  of  heat  units  required  to  evaporate  one  unit  by 
weight  of  water  is  606.5 — 0.6957,  in  which  T  is  the  temperature 
above  that  of  melting  ice.  Hence  it  decreases  with  increase  of 
temperature,  and  in  the  case  of  boiling  water,  in  which  r  =  100°, 
it  becomes  536.  This  means  that  at  the  boiling  temperature 
the  heat  which  is  used  in  the  transformation  of  water  into  vapor 
would  heat  536  units  of  water  at  the  zero  temperature  by  one 
degree.  Condensation  being  the  reverse  of  evaporation,  where 
the  vapor  in  the  air  is  gradually  condensed  in  ascending,  each 
unit  by  weight  of  vapor  condensed  gives  out  a  certain  amount 
of  heat,  varying  a  little  by  the  preceding  expression  with  the 
temperature. 

From  an  inspection  of  Table  II  it  is  seen  that  the  colder 
the  air  the  less  is  its  capacity  for  moisture,  and  also  the  less  is 
this  decreased  by  a  given  decrease  of  temperature.  For  in- 
stance, at  the  temperature  of  30°  the  vapor  tension  of  saturation 
by  the  table  is  23.5i7mm,  and  in  the  ascent  of  the  air  and  cool- 
ing down  to  25°  the  tension  is  diminished  to  I7.363mm  by  con- 
densation. But  when  saturated  air  has  a  temperature  of  only 
5°  the  vapor  tension  is6.5O7mm;  and  in  ascending  and  cooling 
down  to  o°  the  tension  is  reduced  by  condensation  to  4.569mm, 
and  so  is  decreased  by  i.938mm  only,  and  consequently  there  is 
in  this  case  a  much  less  amount  of  vapor  condensed  than  in  the 
other  for  the  same  decrease  of  temperature.  Since,  therefore, 
the  rate  of  decrease  of  temperature  with  increase  of  altitude  in 
the  case  of  no  condensation  is  the  same  at  all  altitudes  and  for 
all  temperatures,  and  the  amount  of  condensation  and  of  latent 
heat  given  out  for  the  same  amount  of  cooling  is  much  less  for 
the  lower  than  for  the  higher  temperatures,  in  the  ascent  of 
saturated  air  at  very  low  temperatures,  such  as  generally  prevail 
in  the  winter  season,  and  at  all  seasons  in  high  altitudes,  the 
rate  of  cooling  with  increase  of  altitude  in  ascending  air  is 


30   CONSTITUTION  AND  NA  TURE   OF  THE  A  TMOSPHERE. 

much  greater  than  it  is  in  the  summer  season,  since  in  the 
former  the  latent  heat  given  out  is  much  less  and  the  rate  be- 
comes more  nearly  that  of  ascending  dry  or  unsaturated  air, 
namely,  about  one  degree  for  each  100  meters. 

The  rate  of  cooling  in  ascending  saturated  air  also  depends 
upon  the  density  of  the  air  and  consequently  upon  the  altitude. 
At  high  altitudes  the  rate  of  condensation  in  ascending  satu- 
rated air,  for  the  same  temperatures,  is  the  same  as  at  low  alti- 
tudes for  equal  volumes,  and  consequently  the  rate  with  which 
heat  is  given  out  as  the  air  ascends  is  the  same  in  both  cases ; 
but  at  high  altitudes,  where  the  density  is  less,  the  same  amount 
of  latent  heat  given  out  in  condensation  gives  rise  to  a  greater 
increase  of  temperature,  the  heating  being  inversely  as  the 
density;  and  hence  at  these  altitudes,  at  the  same  temperatures, 
the  rate  of  decrease  of  temperature  in  ascending  air  is  less, 
since  the  same  volumes  of  air  there  are  heated  more  by  the 
same  amount  of  condensation.  In  the  higher  altitudes,  how- 
ever, the  temperature  is  usually  much  less,  and  on  this  account 
the  rate  of  decrease  of  temperature  above  is  not  nearly  so  much 
diminished  as  it  would  be  if  the  temperature  there  were  the 
same  as  at  lower  altitudes. 

After  the  saturated  air  has  ascended  to  an  altitude  where  it 
has  cooled  down  to  the  temperature  of  o°,  the  vapor  is  then 
condensed  into  snow,  and  by  this  an  additional  amount  of  latent 
heat  is  given  out  equal  to  that  of  liquefaction,  which  is  79.25 
.heat  units  for  each  unit  of  weight  of  liquid,  and  so  is  about  one 
seventh  of  that  given  out  in  the  condensation  of  the  vapor  into 
rain.  This  diminishes  a  little  the  rate  of  cooling  above  the 
plane  of  incipient  freezing. 

Where  there  are  rain-drops  and  fine  cloud-particles  carried 
up  above  this  plane,  as  there  always  are  more  or  less  in  ascend- 
ing currents,  the  rate  of  cooling  is  still  further  diminished  by  the 
latent  heat  given  out  in  freezing,  until  all  are  completely  frozen, 
and  this  rate  may  even  be  sensibly  suspended  for  some  little 
distance  above  this  plane,  where  the  water  particles  carried  up 
are  very  fine,  and  so  thoroughly  diffused  through  the  air  that  the 
Jieat  given  out  is  almost  instantly  communicated  to  all  parts, 


DYNAMICAL  HEATIXG  A. YD    COOLIXG   OF   THE  AIR.      31 

for  until  the  drops  and  fine  particles  are  completely  frozen  they 
must  remain  at  the  temperature  of  o°. 

In  descending  currents  of  air,  even  if  it  is  saturated  at  the 
start,  the  rate  with  which  it  becomes  heated  with  decrease  of 
altitude  is  in  all  cases  the  same  as  that  of  dry  air  —  about  one 
degree  for  each  100  meters;  for  if  it  is  saturated  it  at  once  be- 
comes unsaturated  as  it  descends  and  becomes  warmer,  and 
consequently  there  is  no  condensation,  and  the  rate  is  in  no 
way  affected  by  latent  heat  becoming  sensible,  as  in  the  case 
of  ascending  saturated  air.  Where  the  saturated  air  is  cloud- 
ed, the  clouds  consisting  of  very  small  droplets  of  condensed 
vapor,  these,  after  the  air  in  descending  becomes  unsaturated, 
are  gradually  evaporated,  and  the  heat  of  evaporation  taken 
from  the  air  causes  the  rate  of  increase  of  temperature  in 
descending  to  be  a  little  less  than  that  of  unsaturated  and  clear 
air,  until  the  cloud  particles  are  all  evaporated  and  the  air 
becomes  clear. 

27.  The  theoretical  formula  for  computing  the  rates  of 
-decrease  of  temperature  of  saturated  ascending  air  with  increase 
of  altitude,  for  the  different  conditions  with  regard  to  temper- 
ature and  altitude,  is  too  complex  to  be  investigated  here,  but 
these  rates  are  given  in  Table  III  of  the  Appendix  correspond- 
ing to  the  temperatures  at  the  heads  of  the  columns,  and  the 
pressures  in  the  first,  and  the  approximate  altitudes  in  the  last, 
column  of  the  table.5 

It  has  been  explained  in  §  26  that  the  rate  of  decrease  must 
be  greater  for  the  same  pressures  and  altitudes  in  the  case  of 
low  than  in  those  of  high  temperatures,  and  also,  that  for  the 
same  temperatures  the  rates  must  be  greater  near  the  earth's 
surface  than  at  considerable  altitudes.  It  is  seen  from  an  in- 
spection of  the  computed  rates  in  the  table  that  this  is  the 
case ;  for  at  the  earth's  surface  for  a  temperature  of  — 10°  this 
rate  is  twice  as  great  as  it  is  for  a  temperature  of  30°,  and  the 
rates  also  for  the  same  temperature,  are  much  less  above  than 
at  the  earth's  surface. 

From  Table  III  we  readily  compute  the  temperature  of 
rapidly  ascending  saturated  air  at  any  given  altitude  when  it  is 


32    CONSTITUTION  AND  NATURE   OF   THE   ATMOSPHERE. 

known  at  the  earth's  surface  or  any  other  lower  level.  For 
instance,  suppose  the  temperature  at  the  earth's  surface  is  30°, 
and  the  temperature  of  the  ascending  current  is  required  at  the 
altitude  of  4000  meters  (2.5  miles  nearly).  It  is  seen  from  the 
table  that  the  rate  of  decrease  at  the  earth's  surface  at  that 
temperature  is  o°.37  per  100  meters,  and  that  this  is  very  nearly 
the  rate  at  all  altitudes  in  its  ascent,  since  the  air  as  it  ascends 
gradually  becomes  cooler.  It  can  therefore  be  assumed  to  be 
the  same  in  getting  approximate  values  of  the  rate  of  decrease 
of  temperature  at  the  altitude  of  4000  meters.  The  temper- 
ature, therefore,  at  the  altitude  of  4000  meters  is  decreased 
approximately  o°.37  X  40  —  I4°.8,  and  hence  the  approximate 
temperature  at  that  altitude  is  30°  —  14°. 8  =  15°. 2.  Corre- 
sponding to  this  temperature  and  the  altitude  4000  meters  the 
table  gives  a  rate  of  decrease  of  o°.39.  Taking  the  average  of 
this  rate  and  that  at  the  earth's  surface,  which  is  o°.38,  we  get 
a  more  correct  decrease  of  temperature  at  the  height  of  4000 
meters,  0.38  X  40  —  15°. 2,  which  being  deducted  from  the  sur- 
face temperature,  30°,  we  get  14°. 8  for  the  temperature  at  that 
altitude. 

Where  the  air  at  the  earth's  surface  or  any  of  the  lower 
strata  of  the  atmosphere  is  not  saturated  with  aqueous  vapor, 
but  only  becomes  so  after  having  ascended  to  a  certain  alti- 
tude, the  rate  of  decrease  before  arriving  at  this  altitude  is 
o°.98  per  100  meters  of  ascent.  This  altitude  is  where  the  air 
in  ascending  becomes  cooled  down  to  the  dew-point  which  it 
has  after  having  reached  that  altitude,  which  is  lower  than  the 
dew-point  of  the  lower  level  from  which  it  has  ascended,  since 
the  vapor  tension  of  the  lower  level  is  decreased  from  expan- 
sion, and  this  in  the  ratio  of  the  decrease  of  air-pressure.  The 
vapor  tension  at  the  lower  level  being  given,  the  dew-point  of 
the  level  of  incipient  condensation  is  that  temperature  of 
Table  II  corresponding  to  this  tension  diminished  in  the  ratio 
of  the  pressures  of  the  two  levels.  The  ratio  between  these 
pressures,  and  also  the  amount  of  cooling  of  the  air  in  ascend- 
ing, depend  upon  the  height  of  ascent,  and  this  for  the  plane 
of  incipient  condensation  is  determined  by  the  condition  that 


DYNAMICAL   HEATING- AND    COOLING   OF    THE  AIR.       33 

the  air  in  ascending  must  be  cooled,  at  the  rate  of  o°.98  for 
each  100  meters,  down  to  the  new  dew-point.  The  altitude 
which  satisfies  this  condition,  where  the  temperature  of  the 
air  T,  and  the  depression  of  the  dew-point  T  —  d  are  given, 
cannot  be  determined  directly,  but  only  by  approximations. 
These  altitudes,  so  determined,  corresponding  to  the  air  tem- 
peratures at  the  heads  of  the  columns  and  the  depressions  of 
the  dew-point  in  the  first  column,  are  given  in  Table  IV. 

It  is  seen  that  these  altitudes  are  nearly  independent  of  the 
air  temperatures,  being  only  a  little  less  for  freezing  tempera- 
tures than  for  high  summer  temperatures.  They  are  also- 
entirely  independent  of  the  air-pressure,  so  that  the  lower 
level  may  be  either  sea-level  or  of  any  high  plateau,  or  high 
level  in  the  open  air  above  the  earth's  surface. 

It  is  also  seen  that  if  the  depression  of  the  dew-point,. 
T  —  d,  is  multiplied  into  125,  we  have  approximately  the  alti- 
tudes in  the  table,  especially  for  the  lower  altitudes.  A 
convenient  rule,  therefore,  for  determining  the  altitude  approxi- 
mately in  meters,  is  to  add  one  fourth  part  to  the  depression 
of  the  dew-point  in  Centigrade  degrees  and  multiply  by  100. 
For  instance,  if  the  difference  between  the  air  temperature  and 
the  dew-point  were  10°,  then  the  air  would  have  to  ascend 
about  1250  meters  before  it  would  become  saturated,  and  con- 
densation would  take  place,  and  only  after  this  altitude  would 
be  reached  would  the  rate  of  decrease  of  temperature  be  as. 
given  in  Table  III,  and  the  amount  of  decrease  of  temperature 
through  the  remaining  difference  of  altitude  be  obtained  as. 
in  the  preceding  example. 

It  must  be  understood  that  the  rate  of  cooling  which  has. 
been  given  for  ascending  dry  or  unsaturated  air,  as  likewise  the 
rates  given  in  Table  III,  are  applicable  in  the  case  only  in  which 
the  ascent  of  air  is  so  rapid  that  it  does  not  have  time  to  be 
sensibly  affected  in  other  ways  than  by  expansion  and  the  latent 
heat  of  condensation. 

The  observed  rate  of  decrease  of  temperature  with  increase 
of  elevation  in  the  lower  part  of  the  atmosphere  has  been  found 
to  be  op.6o  for  each  100  meters  on  the  average  for  all  localities 


34   CONSTITUTION  AND  NATURE   OF   THE   ATMOSPHERE. 


and  seasons  of  the  year,  but  this  rate  varies  considerably  in  dif- 
ferent places,  and  is  thought  to  be  in  general  a  little  greater  in 
the  lower  than  in  the  higher  latitudes,  and  it  is  also  consider- 
ably greater  in  summer  than  in  winter.  In  the  latter  season, 
and  especially  at  night  in  the  lower  strata  of  the  atmosphere  in 
the  interior  of  the  continents,  it  not  only  becomes  very  small, 
but  may  even  be  reversed,  so  that  there  is  an  increase  instead 
of  a  decrease  with  increase  of  altitude. 

The  following  table,  given  by  Dr.  Hann,  contains  the  rates  of 
decrease  of  temperature  in  summer  as  deduced  from  Glaisher's 
observations  during  balloon  ascensions  : 

DIMINUTION   OF  TEMPERATURE  PER    IOO   METERS   IN   CELSIUS 

DEGREES. 


WEATHER. 

Altitudes  in  thousands  of  English  feet. 

0-1 

1-2 

2-3 

3-4 

4-5 

5-io 

10-15 

15-20 

Clear. 
Cloudy. 

0.98 

0.86 

0.71 
0-73 

0.55 
0.73 

0.55 
0.56 

0.55 
0-55 

0.46 
0.45 

0-39 
0.40 

0.30 

0.25 

STABLE  AND   UNSTABLE   EQUILIBRIUM. 

28.  If,  when  a  portion  of  the  atmosphere  in  a  state  of  static 
equilibrium  receives,  from  any  slight  temporary  cause  of 
disturbance,  an  upward  or  a  downward  motion,  the  changed 
conditions  arising  from  such  a  movement  tend  to  bring  it  back 
again  to  its  original  position,  it  is  said  to  be  in  a  state  of  stable 
equilibrium,  since,  immediately  after  such  disturbance,  the  part 
disturbed  is  brought  back  and  soon  settles  in  its  original  posi- 
tion. But  if,  after  any  such  disturbance,  the  changed  condition 
tends  to  continue  the  motion  and  to  increase  the  velocity  of  the 
air  disturbed  in  the  direction  in  which  it  was  started,  either  up- 
ward or  downward,  the  atmosphere  is  then  said  to  be  in  a  state 
•of  unstable  equilibrium,  since  although  in  static  equilibrium  as 
long  as  it  is  not  disturbed,  yet  the  slightest  disturbance  intro- 
duces an  initial  change  in  the  conditions,  which  tends  to  con- 


STABLE  AND    UNSTABLE   EQUILIBRIUM.  35 

tinue  the  motion,  until  by  a  complete  inversion  of  the  strata  of 
the  atmosphere,  or  from  some  other  cause,  the  conditions  are  so 
changed  that  the  state  of  stable  equilibrium  is  brought  about. 

It  is  well  known  that  if  any  portion  of  a  fluid,  or  a  solid  im- 
mersed in  a  fluid,  has  a  less  density  than  the  surrounding  part 
of  the  fluid  at  the  same  level,  it  tends  to  rise  up,  and  if  not  hin- 
dered, continues  to  rise  until  it  comes  to  the  top ;  but  if,  on 
the  other  hand,  it  has  a  greater  density,  it  sinks  down  to  the 
bottom.  So  if,  when  any  portion  of  the  atmosphere  receives 
.an  upward  motion,  its  density  becomes  greater,  or  a  downward 
motion,  less,  than  that  of  the  surrounding  air  at  the  same  level, 
it  at  once  comes  back  to  its  former  position  after  the  tempo- 
rary cause  of  disturbance  ceases ;  but  if,  in  rising  up,  the  den- 
sity becomes  less,  or  in  sinking  down,  greater,  than  that  of  the 
surrounding  parts  of  the  same  level,  the  tendency  is  to  continue 
on  in  the  direction  in  which  it  is  started.  In  the  former  case  it 
is  in  a  state  of  stable,  and  in  the  latter  of  unstable,  equilibrium. 
But  since  a  difference  of  density  in  these  cases  depends  mostly, 
if  not  entirely,  upon  a  difference  of  temperature  of  the  ascend- 
ing or  descending  air  and  that  of  the  surrounding  part  of  the 
atmosphere  at  the  same  level,  the  state  of  stable  or  unstable 
equilibrium  depends  very  much  upon  the  relation  between 
the  rate  of  decrease  of  temperature  with  increase  of  altitude  in 
the  surrounding  undisturbed  part  of  the  atmosphere  and  that  of 
the  ascending  or  descending  current. 

29.  We  have  seen  that  the  temperature  of  rapidly  ascending 
•unsaturated  air  decreases  very  nearly  one  degree  for  each  100 
meters  of  ascent.  If,  therefore,  the  temperature  of  the  sur- 
rounding undisturbed  part  of  the  atmosphere  decreases  with  in- 
crease of  altitude  at  a  rate  less  than  this,  then  as  the  air,  started 
by  some  slight  temporary  impulse,  ascends,  its  temperature  be- 
comes less,  and  consequently  its  density  greater,  than  that  of 
the  surrounding  undisturbed  air  at  the  same  level ;  and  hence 
the  motion  is  soon  arrested  and  reversed,  and  the  air  after  a  few 
oscillations  is  brought  by  friction  to  a  state  of  rest  in  its  origi- 
nal position.  For  instance,  let  us  suppose  that  the  arrange- 
ment of  temperature  with  regard  to  altitude,  of  a  dry  or  unsatu- 


36    CONSTITUTION  AND  NATURE   OF   THE  ATMOSPHERE. 


rated  and  undisturbed  atmosphere  to  be  represented  in  the 
third  column  of  the  following  table,  in  which  the  first  column 
contains  the  altitudes,  and  the  second  the  temperatures  of  the 
ascending  current  of  air  at  the  altitudes  in  the  first  column : 


Meters. 

3000 

0° 

6° 

-6° 

2500 

5 

10 

o 

2OOO 

IO 

14 

6 

1500 

15 

18 

12 

1000 

20 

22 

18 

5OO 

25 

26 

24 

ooo 

30 

30 

30 

The  temperature  of  the  ascending  column  is  here  supposed 
to  decrease  exactly  i°  for  each  100  meters.  It  is  readily  seen 
that  with  the  arrangement  of  temperature  in  the  third  column 
a  slight  upward  motion  of  air  at  any  place  would  cause  its  tem- 
perature at  all  altitudes  to  be  a  little  less  and  consequently  its 
density  a  little  greater  than  that  of  the  surrounding  undisturbed 
air  at  the  same  levels,  and  this  would  continue  to  increase  as  the 
air  ascends,  until  the  temperatures  would  finally  be  as  in  the 
second  column  of  the  preceding  table,  if  the  ascent  were  "to  con- 
tinue. But  this  increased  pressure  of  the  whole  column  having 
an  ascending  motion  would  soon  bring  it  back.  It  would  then 
descend  a  little  lower  than  its  original  undisturbed  position, 
and  in  so  doing  it  is  readily  seen  that  the  temperature  then 
would  be  greater  and  the  density  less  than  that  of  the  sur- 
rounding undisturbed  air,  and  the  further  it  descended  below 
this  position,  the  more  so,  and  hence  the  downward  motion 
would  soon  be  stopped  and  reversed,  and  after  a  few  oscilla- 
tions it  would  be  brought  to  rest  by  friction  in  its  first  position. 
And  this  would  be  the  case  whatever  the  direction,  upward  or 
downward,  of  the  first  impulse.  Hence  with  this  vertical  dis- 
tribution of  the  temperature,  the  atmosphere  is  in  the  state  of 
stable  equilibrium. 

But  if  we  suppose  the  temperature  to  decrease  with  increase 
of  altitude  at  the  rate  of  i°.2  for  each  100  meters,  instead  of 
o°.8  as  in  the  preceding  case,  we  shall  have  the  vertical  dis- 


STABLE  AND    UNSTABLE  EQUILIBRIUM.  37 

tribution  of  temperature  as  given  in  the  fourth  column  of  the 
preceding  table.  It  is  readily  seen  that  now  a  slight  upward 
motion  would  cause  all  parts  receiving  such  a  motion  to  have  a 
little  greater  temperature  and  less  density  than  those  of  the 
surrounding  undisturbed  parts,  and  the  greater  the  disturbance 
the  less  the  density  relative  to  that  of  the  surrounding  air  at 
the  same  levels.  Hence  there  would  be  no  tendency  to  fall 
back  again,  but  to  continue  on,  and  the  further  the  displace- 
ment the  greater  this  tendency  until  a  regular  ascending  cur- 
rent would  be  established,  in  which  the  temperatures  at  differ- 
ent altitudes  would  be  as  represented  in  the  second  column 
of  the  preceding  table.  The  difference  of  temperature,  then, 
between  the  ascending  air  and  the  surrounding  quiet  air  would 
increase  one  degree  for  each  500  meters,  so  that  at  the  altitude 
of  1500  meters  it  would  be  3°,  at  3000  meters  6°,  and  so  on; 
and  consequently  there  would  be  a  strong  tendency  to  rush  up 
to  the  top  of  the  atmosphere,  at  least  if  the  same  vertical 
decrease  of  temperature  in  the  undisturbed  atmosphere  should 
extend  all  the  way  up.  If  the  initial  motion  were  downward, 
the  temperature  would  become  less  and  the  density  greater 
than  in  the  surrounding  air  at  the  same  level,  and  hence,  being 
•once  started,  the  tendency  would  be  to  continue.  In  this  case, 
however,  the  down-rushing  air  could  not  escape  so  readily  on 
account  of  the  friction  of  the  earth's  surface  in  its  lateral  escape 
at  the  surface.  Without  some  initial  disturbance,  however, 
either  upward  or  downward,  the  atmosphere  would  remain  at 
rest.  With  the  vertical  distribution  of  temperature,  therefore, 
given  in  the  last  column  of  the  table,  if  the  air  should  receive  a 
start,  either  upward  or  downward,  the  tendency  would  be  to 
continue  on,  and  hence  with  this  distribution  the  atmosphere 
is  in  the  state  of  unstable  equilibrium. 

If  the  vertical  temperature  gradient  in  the  undisturbed 
atmosphere  is  such  that  the  temperature  decreases  i°  for  each 
100  meters  of  increase  of  altitude,  then  the  atmosphere  is  said 
to  be  in  the  indifferent  state  of  equilibrium. 

30.  Again,  let  us  imagine  a  portion  of  air  confined  within  a 
balloon  of  very  fine  silk,  the  weight  of  which  would  be  insensible 


38    CONSTITUTION  AND  NATURE   OF   THE  ATMOSPHERE. 

in  comparison  with  the  weight  of  the  confined  air.  If  the 
decrease  of  the  temperature  of  the  air  with  increase  of  altitude 
were  i°.2  for  each  100  meters,  then  the  air  in  the  balloon  in  its 
ascent,  its  initial  temperature  being  supposed  to  be  the  same  as 
that  of  the  surrounding  air,  would  become  o°.2  warmer  than 
the  surrounding  air  for  each  100  meters  of  ascent,  or  one  degree 
for  each  500  meters,  and  after  having  ascended  2000  meters 
would  be  4°  warmer  than  that  of  the  surrounding  air;  so  that 
the  higher  it  would  ascend,  the  stronger  would  be  the  tendency 
to  continue  on.  But  if  the  balloon  were  at  some  altitude  above 
the  earth's  surface  and  started  downward  in  the  same  condition 
of  the  air,  the  air  contained  within  would  become  one  degree 
colder  for  each  500  meters  of  descent,  and  consequently  heavier 
than  the  surrounding  air,  and  so,  being  once  started,  the  ten- 
dency would  be  to  go  on.  Supposing  the  silk  to  have  no  weight, 
and  the  initial  temperature  of  the  air  within  and  without  to  be 
the  same,  there  would  be  no  tendency  to  move  either  up  or 
down  until  once  started  by  some  initial  impulse.  This  would, 
therefore,  be  a  state  of  unstable  equilibrium  for  unsaturated 
air. 

If  the  rate  of  decrease  of  temperature  in  the  air  with  increase 
of  altitude  were  only  o°.8  for  each  100  meters,  then,  it  is  readily 
seen,  the  air  in  the  ascending  balloon  would  become  o°.2  colder 
than  the  surrounding  air  for  each  100  meters  of  ascent,  and  o°. 2 
warmer  for  each  100  meters  of  descent :  so  that  in  the  former 
case  it  would  become  heavier  than  the  surrounding  air,  and  soon- 
cease  to  ascend,  and  then  fall  back  again ;  and  in  the  latter  it 
would  become  lighter,  and  soon  cease  to  fall,  and  would  run  up 
again  to  the  position  which  it  left.  This  would  therefore  be  a 
state  of  stable  equilibrium  for  unsaturated  air. 

It  will  be  readily  understood  from  the  preceding  illustrations 
that  if  an  unsaturated  atmosphere  has  a  temperature  which 
decreases  with  increase  of  altitude  at  a  rate  which  is  less  than 
one  degree  (accurately  o°.98)  for  each  100  meters,  it  is  in  the 
stable  state  ;  but  if  this  rate  is  greater  than  one  degree  for  each 
IOO  meters,  it  is  in  the  unstable  state. 

31.  If  the  ascending  air  is  saturated  with  aqueous  vapor,  it 


CHANGES  OF  ALTITUDE  AND  DENSITY.  39 

is  seen  from  Table  III  that  the  rate  of  decrease  of  temperature 
with  increase  of  altitude  required  to  produce  the  state  of  un- 
stable equilibrium  is  much  less,  and  this  is  especially  the  case 
in  the  summer  season,  and  in  all  seasons  at  great  altitudes. 
For  instance,  in  the  example  given  in  §  27,  the  average  rate  of 
decrease  is  o°.38  for  each  100  meters,  and  the  rate  is  very 
nearly  constant  at  all  altitudes.  If,  therefore,  the  rate  of  de- 
crease in  the  quiet  air  were  only  a  little  greater  than  this,  the 
air  would  be  in  the  unstable  state,  whereas  in  the  case  of  dry 
or  unsaturated  air  the  rate  would  have  to  be  more  than  twice 
as  great.  But  with  a  temperature  of  — 10°  the  rate  of  decrease 
in  ascending  air  is  about  twice  as  great,  and  so  the  rate  of 
decrease  in  the  undisturbed  and  quiet  air  would  have  to  be 
greater  than  this  is,  to  give  rise  to  the  unstable  state,  but  still 
considerably  less  than  in  the  case  of  dry  or  unsaturated  air. 

In  the  case  of  saturated  air  the  initial  motion  of  disturbance 
must  be  upward,  since  when  it  is  downward  the  air  becomes 
warmer,  and  so  at  once  unsaturated,  so  that  the  tendency  to  a 
continued  downward  motion  can  only  take  place,  although  the 
air  at  first  may  be  completely  saturated,  when  the  rate  of 
increase  or  decrease  with  change  of  altitude  in  the  undisturbed 
surrounding  air  is  greater  than  o°.98  for  each  100  meters. 

RELATION  BETWEEN   CHANGES   OF  ALTITUDE  AND  DENSITY. 

32.  In  a  quiet  atmosphere  at  the  temperature  of  o°  C.,  the 
pressure,  and  consequently  the  density,  is  decreased  by  the 
7  0*03  part  for  each  meter  of  increase  of  altitude,  for  in  an  ascent 
through  a  vertical  distance  of  one  meter  this  part  of  the  mass 
is  left  below ;  and  this  is  true  for  all  pressures  and  altitudes,  if 
the  temperature  is  the  same,  since  the  height  of  a  homogeneous 
atmosphere  is  the  same,  whatever  the  mass  and  pressure.  But 
we  have  seen  that  the  volume  of  the  air  at  all  temperatures  is 
increased,  and  consequently  its  density  decreased,  by  the  -^^ 
part  of  that  at  the  temperature  of  o°  C.,  for  each  degree  of 
increase  of  temperature.  Dividing,  therefore,  ^-^3  by  -^,  we 
get  -fffj  =  o°.O348  for  the  decrease  of  temperature  for  each 


40   CONSTITUTION  AND   NA  TURK   OF   THE  A  TMOSPHERE. 

meter  of  increase  of  altitude  required  to  give  the  same  density 
at  all  altitudes. 

For  other  and  higher  temperatures  it  would  be  necessary  to 
ascend  through  a  vertical  distance  of  more  than  one  meter  in 
the  ratio  of  the  absolute  temperatures,  in  order  to  diminish  the 
density  ^Vs"  Part;  and  hence  the  decrease  of  temperature  in 
this  case  would  be  o°.O348  for  a  change  of  altitude  greater  in 
the  same  proportion,  and  the  rate  of  decrease  required  would 
be  inversely  as  the  absolute  temperature. 

THE  VISCOSITY   OF  THE   AIR. 

33.  That  property  of  the  atmosphere,  or  of  any  gas  by  which 
one  stratum  cannot  move  with  greater  velocity  over  another 
without  receiving  resistance  from  it,  is  called  viscosity.  By  the 
kinetic  theory  of  gases  this  arises  from  the  continual  inter- 
change of  molecules  between  the  strata.  Those  of  the  more 
slowly  moving  stratum,  coming  in  contact  with  those  of  the 
contiguous  stratum  moving  with  greater  velocity,  tend  to 
diminish  its  velocity,  while  those  of  the  more  rapidly  moving 
stratum,  coming  in  contact  with  those  of  the  other,  tend  to 
accelerate  its  motion,  so  that  there  is  a  tendency  in  these 
contacts  to  equalize  the  velocities  of  the  two,  but  leaving  the 
whole  amount  of  momentum  in  the  two  strata  unchanged, 
when  there  is  simply  a  mutual  action  between  the  two.  The 
measure  of  viscosity  is  the  amount  of  force  required  per  square 
unit  of  surface  to  overcome  the  mutual  action  of  two  strata 
of  unity  of  thickness  upon  each  other,  and  having  a  relative 
velocity  of  unity.  This  mutual  action  between  the  two,  usually 
called  friction  or  frictional  resistance,  is  proportional  to  the 
relative  velocities  of  the  strata,  and,  according  to  the  deduction 
of  Maxwell  from  the  kinetic  theory  of  gases,  is  independent  of 
density  and  pressure  where  the  temperature  remains  the  same. 

When  the  whole  atmosphere  from  bottom  to  top  moves  in 
the  same  horizontal  direction  with  velocities  increasing  with 
increase  of  altitude,  the  lower  stratum  in  contact  with  the 
earth's  surface  is  retarded  by  the  contacts  of  its  molecules  with 


THE    VISCOSITY  OF   THE  AIR.  41 

the  asperities  of  that  surface,  but  the  motions  of  each  successive 
stratum  above  is  acted  upon  by  the  more  slowly  moving  stratum 
below  and  retarded  in  its  motion,  unless  there  is  some  constantly 
acting  force  to  overcome  the  effect  of  this  frictional  resistance, 
and  maintain  a  constant  relative  velocity  between  the  two 
strata.  If  there  are  three  successive  strata,  of  which  the  relative 
velocity  between  the  first  and  second  is  the  same  as  that  be- 
tween the  second  and  third,  then  the  actions  of  the  first  and 
third  upon  the  intermediate  one  are  precisely  the  same,  but  in 
contrary  directions. 

Since  an  increase  of  temperature  increases  the  velocities  of 
the  interchanging  motions  of  the  molecules  between  the  strata, 
the  viscosity  of  the  atmosphere  is  increased  by  increase  of  tem- 
perature. Experiment  makes  it  about  as  the  three-fourths 
power  of  the  absolute  temperature.' 


CHAPTER  II. 

THE  MOTIONS  OF  BODIES  RELATIVE  TO  THE  EARTH'S 

SURFACE. 

34.  THE  motion  of  a  body  relative  to  the  earth's  surface,, 
called  relative  motion,  whether  this  body  is  set  in  motion  by  a 
single  impulse,  or  is  continually  acted  upon  by  some  force 
other  than  that  of  gravity,  is  very  different  upon  the  earth  with 
a  rotation  upon  its  axis  from  what  it  would  be  if  the  earth  were 
at  rest.     If  the  earth  were  at  rest,  and  spherical,  as  it  would 
have  to  be  in  this  case,  a  body  set  in  motion  in  any  direction 
upon  its  surface,  supposed  to  be  perfectly  smooth  and  without 
friction,  would   continue   to    move   uniformly  with  its  initial 
velocity  in  a  great  circle  of  the  sphere.     But  where  the  earth 
has  a  motion  of  rotation  upon  its  axis,  we  shall  see  that  this  is- 
far  from  being  so,  except  in  the  case  where  the  initial  motion 
is  in  the  line  of  the  equator.     If,  also,  the  earth  were  at  rest,  a 
body  projected  vertically  upward  would  fall  back  to  the  point 
where  it  started,  but  in  the  case  of  the  earth  with  a  rotation 
upon  its  axis,  it  falls  to  the  earth  a  little  west  of  this  point,  and 
projectiles  generally,  started  in  any  direction  relative  to  the 
earth's  surface,  would  have  different  relative  motions  in  the  two 
cases.    In  considering,  therefore,  the  relative  motions  of  bodies 
on  the  earth's  surface,  it  is  very  important  to  take  into  account 
the  influence  of  the  earth's  rotation  upon  such  motions,  and  to 
not  regard  these  as  being  the  same  as  the  absolute  motion  in 
case  of  no  rotation. 

CENTRIFUGAL  FORCE. 

35.  In  determining  the  influence  of  the  earth's  rotation 
upon  relative  motions  upon  and  near  its  surface,  the  centrifugal 
force  arising  from  the  earth's  rotation  comes  in  as  an  impor- 

42- 


CENTRIFUGAL  FORCE. 


43 


tant  consideration.  It  is  necessary,  therefore,  to  understand  at 
the  start,  the  nature  and  law  of  this  force.  If  a  free  body  in 
space  has  a  motion  in  any  direction  and  is  not  acted  upon  by 
any  force,  or  affected  by  any  kind  of  resistance,  frictional  or 
otherwise,  it  continues  to  move  on  with  uniform  velocity  in 
this  direction.  If,  therefore,  a  body  at  a,  Fig.  i,  has,  under 
these  conditions,  a  motion  in  the  direction  of  the  line  ad,  tan- 
gent to  the  circle  aegh,  of  which  o  is  the  centre,  and  has  a 
velocity  which  will  carry  it  to  b  in  a  unit  of  time,  as  one  second, 
then,  at  the  end  of  this  unit  of  time,  it  will  have  departed  from 


the  circumference,  and  have  increased  its  distance  from  the 
centre  o,  by  the  space  eb.  Drawing  now  the  line  cf  tangent 
to  the  circle  at  e,  it  will  perhaps  be  evident  to  most  readers, 
without  a  rigorous  demonstration,  that  the  angle  dcf  at  the 
intersection  of  the  two  tangents  to  the  circle  at  a  and  at  e  is 
equal  to  the  angle  aoe,  since  at  the  start  as  the  movable  radius 
oe  changes  its  direction  with  regard  to  oa,  the  tangent  at  e  must 
change  its  direction  with  reference  to  that  of  ad  at  the  same 
rate.  In  the  case  of  very  small  angles  between  two  lines  form- 
ing an  angle  as  cd  and  cf,  the  rates  at  which  a  body  moving: 
along  one  of  them  with  a  given  velocity  departs  in  different 


44    MOTIONS    OF  BODIES  RELATIVE    TO  EARTH'S  SURFACE. 

cases  from  the  other  are  sensibly  proportional  to  the  angles 
between  them.  The  body  then,  in  moving  from  a  towards  d 
with  a  given  uniform  velocity,  will,  at  the  ends  of  different 
units  of  time,  if  the  unit  is  very  small,  and  this  is  entirely  arbi- 
trary, depart  from  the  line  cf  and  from  the  centre  of  the  circle 
with  velocities  which  are  proportional  to  the  angle  dcf  at  the 
ends  of  these  units  of  time,  and  consequently  proportional  to 
the  angle  aob  which  is  proportional  to  the  time  ;  for  while  the 
angle  aob  is  small  it  is  proportional  to  ab,  which,  since  the  body 
moves  with  uniform  velocity,  is  proportional  to  the  time.  The 
law  of  departure,  then,  for  very  small  arcs,  is  that  the  rate  or 
velocity  of  departure  of  the  body  from  the  circumference  of 
the  circle  and  from  the  centre,  is  proportional  to  the  time 
elapsed. 

If  a  body  is  free  and  is  acted  upon  by  any  constant  force, 
as  that  of  gravity,  its  motion  is  accelerated  in  proportion  to  the 
time,  the  increase  of  velocity  in  a  unit  of  time  being  called  the 
acceleration.  For  instance,  a  body  near  the  earth's  surface, 
acted  upon  by  the  force  of  gravity,  acquires  a  velocity  of  about 
32  feet  per  second  at  the  end  of  the  first  second,  64  feet  at  the 
end  of  the  second  second,  and  so  on  ;  the  velocity  continuing 
to  be  increased  in  proportion  to  the  time.  Now  we  have  seen 
above  that  in  the  motion  of  a  body  in  the  direction  of  a  tangent 
to  the  circumference  of  a  circle  the  law  of  departure  from  the 
circumference  and  from  the  centre  of  the  circle  is  precisely  the 
same  as  that  of  a  falling  body,  or  of  any  body  acted  upon  by  a 
given  uniform  force,  the  velocities  acquired  in  both  cases  being 
in  proportion  to  the  time.  The  tendency,  therefore,  of  a  body 
at  a  to  depart  from  the  centre  is  exactly  similar  to  the  action 
of  any  force  in  a  given  direction  in  causing  a  body  to  move 
from  its  initial  position.  And  if  a  body  at  a,  with  a  motion  in 
the  direction  of  ad,  is  constrained  to  move  in  the  circumference 
of  the  circle  toward  e,  as  in  a  groove,  or  in  consequence  of 
being  attached  to  the  centre  o  by  a  cord,  corresponding  to  the 
radius  of  the  circle,  the  pressure  against  the  side  of  the  groove 
in  the  one  case,  and  the  tension  of  the  cord  in  the  other,  are  the 
same  as  the  pressure  which  would  arise  from  the  action  of  any 


CENTRIFUGAL  FORCE.  45 

force  on  a  body  of  the  same  mass  if  it  were  such  as  to  cause  an 
acceleration  in  the  body,  if  free  to  move,  equal  to  that  of  the 
rate  of  departure  of  the  moving  body  from  the  centre  of  the 
circle.  This  tendency  of  a  body,  in  gyrating  around  a  centre, 
to  recede  from  the  centre,  and,  when  not  free  to  depart,  to 
cause  pressure  in  the  direction  of  the  radius  from  the  centre,  is 
called  centrifugal  force.  It  must  be  understood,  however,  that 
this  so-called  force  is  not  a  real  force,  such  as  arises  from  any 
attracting  or  propelling  force  in  a  given  direction,  but  simply 
that  the  gyrating  body,  if  free,  would  at  any  given  instant  be 
carried  away  from  the  centre  by  its  inertia  in  the  varying  direc- 
tion of  the  radius,  in  the  same  manner  as  it  would  be  moved  in 
a  given  direction  by  the  action  of  a  constant  and  real  force  in 
this  direction.  The  centrifugal  force  depends  simply  upon  the 
inertia  of  the  body,  and  being  always  at  right  angles  to  the 
direction  of  the  gyratory  motion,  it  does  not  increase  velocity 
and  momentum,  as  a  real  force  does,  but  tends  simply  to  drive 
a  body  away  from  the  centre  of  curvature,  and  to  cause  pressure 
in  that  direction. 

36.  The  effect  of  centrifugal  force  with  reference  to  the 
varying  distance  of  the  body  along  a  radius  of  constantly  vary- 
ing direction  being  similar  to  that  of  a  real  force  with  reference 
to  the  motion  of  the  body  along  a  fixed  direction,  we  obtain  an 
expression  of  this  force  in  the  same  manner,  namely,  by  multi- 
plying the  mass  of  the  body  into  its  rate  of  departure  from  the 
centre  at  the  end  of  a  unit  of  time,  corresponding  to  what  is 
called  acceleration  in  the  case  of  a  real  force.  In  the  case  of 
the  centrifugal  force,  however,  it  must  be  understood  that  the 
unit  of  time,  which  is  entirely  arbitrary,  must  be  so  small  that 
the  body  describes  only  a  very  small,  strictly  infinitely  small,, 
arc  in  comparison  with  the  whole  circumference  of  a  circle 
during  this  time. 

In  a  falling  body,  if  the  unit  of  time  is  one  second,  the 
velocity  at  the  beginning  of  the  first  unit  is  o,  and  at  the  end 
of  it  32  feet ;  and  as  the  velocity  increases  in  proportion  to  the 
time,  the  average  velocity  is  16  feet.  Consequently  the  space 
fallen  through  during  the  first  second  is  16  feet,  one  half  the 


46    MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S    SURFACE. 

velocity  acquired  at  the  end  of  the  second.  If  now,  in  Fig.  i, 
-we  suppose  ab  to  be  the  space  passed  over  by  the  body  in  a 
unit  of  time,  this  unit  being  such  that  ab  is  very  small  in  com- 
parison with  the  radius  ao,  or  the  whole  circumference  of  the 
circle,  though  it  is  necessarily  very  much  exaggerated  as  repre- 
sented in  the  figure,  then  be  is  the  space  over  which  the  body 
passed  during  this  unit  of  time  in  the  varying  direction  of  the 
radius  from  the  centre,  or  the  space  by  which  the  distance  of 
the  body  from  the  centre  is  increased.  Consequently,  from  what 
has  just  been  stated  in  the  case  of  a  falling  body,  2be  is  the 
acceleration  of  the  centrifugal  force.  Putting,  therefore,  as 
usual,  m  for  the  mass  of  the  body,  we  have  2be  X  m  for  the  ex- 
pression of  the  centrifugal  force. 

But  it  is  desirable  to  have  an  expression  of  this  force  in 
terms  of  the  gyratory  velocity  of  the  body  around  the  centre 
of  gyration,  and  the  distance  of  the  body  from  the  centre.  The 
gyratory  velocity  of  a  body  is  its  velocity,  or  that  component 
of  its  velocity,  which  is  at  right  angles  to  the  radius  of  gyration. 
If  the  body  at  a,  Fig.  I,  has  a  velocity  which  would  carry  it  to 
b  in  a  unit  of  time,  then  the  distance  ab,  sensibly  equal  to  the 
arc  ae,  is  its  gyratory  velocity  at  the  point  a.  The  gyratory 
velocity  a'b'  of  any  point  a'  in  the  radius  ao,  at  the  distance  of 
unity  from  the  centre  o,  expressed  in  terms  of  this  unit,  is  called 
the  gyratory  velocity  in  terms  of  the  radius,  since  this  would  be 
the  real  gyratory  velocity  if  the  radius  were  made  the  measur- 
ing unit.  It  is  the  ratio  between  the  gyratory  velocity  and  the 
radius,  since  it  is  the  gyratory  velocity  divided  by  the  radius, 
and  so  expressed  it  is  often  called  simply  angular  velocity,  since 
it  is  proportional  to  the  rate  of  change  of  the  angle  at  the 
centre.  The  real  gyratory  velocity,  therefore,  is  equal  to  the 
gyratory  velocity  in  terms  of  the  radius  multiplied  into  the 
radius.  Denoting  the  gyratory  velocity  ab,  Fig.  I,  by  w,  the 
radius  ao  by  r,  and  the  gyratory  velocity  in  terms  of  the  radius 
by  n,  we  evidently  have  ab  =  ao  x  n,  or  w  =  rn. 

We  have  in  the  figure,  as  has  been  shown,  the  angle  bee 
equal  the  angle  aob ;  and  hence  be  is  evidently  as  many  times 
greater  than  ce  as  ab  is  greater  than  ao,  and  as  ab  or  w  is  equal 


CENTRIFUGAL   FORCE.  47 

to  rn,  be  is  equal  to  ce  X  n,  and  so  2be  is  equal  to  2ce  X  n.  But 
<r^  is  equal  to  ac  or  one  half  of  ab,  where  all  are  very  small,  as 
here  supposed,  and  consequently  2ce  is  equal  to  ab  or  w,  and 
hence  we  have  2ce  =  w  =  rn.  Putting  rn  for  2ce  in  the  preced- 
ing expression  of  2be,  we  have  2be  =  rn  X  n  =  rn*,  and  the  pre- 
ceding expression  of  the  centrifugal  force,  2be  x  m,  becomes 
•rn*m.  Or  putting  Fc  for  the  centrifugal  force,  we  have* 

77  9  W* 

Fc  =  rtfni  —  —  m. 
r 

The  last  form  of  this  expression  is  obtained  from  the  first  one 
by  putting  rn*  =  rn  X  n,  and  then  for  rn  and  n  their  equals  w 
and  w/r.  From  the  last  form  of  expression  it  is  seen  that  the 
centrifugal  force  is  directly  as  the  square  of  the  gyratory  veloc- 
ity and  inversely  as  the  distance  of  the  body  from  the  centre 
of  gyration. 

In  obtaining  the  preceding  results  it  was  assumed  that  the 
unit  of  time  is  very  small  (strictly  it  should  be  infinitely  small), 
but  the  expressions  thus  obtained  are  applicable  to  any  other 
unit.  For  velocity  expresses  simply  the  relation  between  an 
infinitely  small  portion  of  space  passed  over  by  the  body  at  any 
instant  of  time  and  the  corresponding  infinitely  small  portion 
of  time,  and  this  can  be  expressed  by  using  either  large  or 
small  units  of  time,  it  being  understood  that  the  space  passed 
over  during  the  unit  of  time  is  that  which  would  result  from  a 
continuance  of  the  rate  of  motion  or  relation  between  the 
infinitely  small  portions  of  space  and  time  at  any  instant 
through  the  whole  unit  of  time,  however  large  it  may  be. 


*  Joining  e  and^-  in  the  figure,  and  considering  the  arc  ac  a  straight  line,  and 
•be  a  continuation  of  the  line  ge,  as  we  may  when  they  are  very  small,  we  have 
by  the  well-known  proportions  of  similar  triangles  eg  :  ae  : :  ae  :  be  ;  or  putting 

fib  =  ae,  as  we  can  where  these  quantities  are  very  small,  we  have  be  •=  .     '  • 

-w>  CZ 

or  2be  =  —  ,  since  where  ae  is  very  small  we  have  sensibly  eg  =  ag=  2r.     Hence, 

multiplying  this  expression  of  the  acceleration  ibe  into  the  mas«  m,  we  get  the 
expression  of  the  centrifugal  force  above. 


48     MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACE.. 

37.  If  the  body  is  forced  to  move  in  an  irregular  curve,  as 
in  a  groove,  which  is  not  the  circumference  of  a  circle,  there  is 
always  some  circle  the  circumference  of  which  coincides  sensibly 
with  a  very  small  portion  of  this  irregular  curve  at  any  point 
where  the  body  may  be  moving,  and  the  radius  of  this  circle  is 
called  the  radius  of  curvature.  Since  the  preceding  expression 
of  centrifugal  force  is  deduced  from  the  consideration  of  only 
a  very  small  portion  of  the  circumference  of  the  circle,  strictly 
only  an  infinitely  small  part,  and  is  dependent  simply  upon  the 
curvature  at  that  point,  it  is  evident  that  it  is  applicable  to  any 
point  of  an  irregular  curve,  if  we  use  for  r  in  the  expression  the 
radius  of  curvature  of  that  point  of  the  curve.  Hence,  the 
velocity  remaining  the  same,  the  centrifugal  force  is  inversely 
as  the  radius  of  curvature. 

As  an  expression  of  the  ratio  between  the  centrifugal  force 
and  that  of  gravity,  where  both  forces  act  upon  the  same  or 
equal  masses,  we  get  from  the  preceding  expression,  by  divid- 
ing by  gm,  the  force  of  gravity, 


gm  9.806^ 

in  which  the  units  are  the  second  of  time  and  the  meter.  If 
the  English  foot  is  used  as  the  unit  of  length  instead  of  the 
meter,  then  32.2  instead  of  9.806  must  be  used  as  the  numerical 
coefficient  of  r  in  the  denominator  of  the  expression. 

As  an  example  of  the  practical  application  of  this  relation, 
let  us  suppose  that  the  body  has  a  velocity  on  a  horizontal 
plane  of  20  meters  per  second  (45  miles  per  hour  nearly*),  and 
that  it  is  constrained  to  move  in  a  curve  with  a  radius  of  curva- 
ture at  any  given  point  of  1000  meters.  We  then  have  for  the 
ratio  of  the  centrifugal  force  to  that  of  gravity  at  that  point 
202:  (1000  X  9.806)  =  0.0408.  If,  therefore,  the  moving  body 
were  that  of  a  railroad  car,  with  a  velocity  of  20  meters  per 
second,  on  a  part  of  the  road  having  a  radius  of  curvature  of 

*To  reduce  meters  per  second  to  miles  per  hour,  multiply  by  2.237,  and  vice 
•versa. 


CENTRIFUGAL   FORCE.  49 

1000  meters,  the  lateral  pressure  ofi  the  side  of  the  rails,  in  a 
direction  from  the  centre  of  curvature,  would  be  about  the  -^ 
part  of  the  vertical  pressure  of  the  car. 

38.  If  the  body  is  entirely  free,  and  is  not  constrained  to 
move  in  a  given  path,  but  is  acted  upon  by  some  centripetal 
force  which  is  exactly  equal  to  the  centrifugal  force,  it  in  this 
case  moves  concentrically  around  the  centre  of  the  forces  in  the 
circumference  of  a  circle.  Such  a  force  may  be  found  in  the 
one  component  of  the  force  of  gravity  where  the  body  gyrates 
horizontally  upon  a  surface  having  a  descending  gradient  on  all 
sides  from  the  exterior  part  toward  the  centre  of  gyration. 
The  measure  of  such  a  gradient  is  the  ratio  between  the  change 
of  level  in  a  given  horizontal  distance,  and  this  distance.  For 
instance,  if  the  change  of  level  is  one  meter  in  the  distance  of 
1000  meters,  the  gradient  is  o.ooi,  or  one  in  one  thousand,  what 
ever  the  unit  of  measure.  If  the  body  in  moving  rises  to  a 
higher  level,  it  is  called  an  ascending  gradient,  and  vice  versa. 

The  ratio  expressing  the  gradient  is  also  that  between  the 
component  of  gravity,  acting  in  any  direction  along  the  inclined 
surface,  and  the  whole  force  of  gravity.  If  de  in  Fig.  2  is  the 
change  of  level  in  the  horizontal  distance  ad,  if  we  denote  the 
ratio  expressing  the  gradient  by  e  we  shall  have  e  =  de  :  ad. 
If  now  we  let  the  vertical  line  ce  represent  the  force  of  gravity, 
and  cb  is  drawn  perpendicular  to  the  inclined  surface,  then,  by 
the  principle  of  the  resolution  of  forces,  the  whole  force  of 
gravity  represented  by  ce  is  equivalent  to  two  other  forces^ 
called  components,  one  of  which  is  represented  by  the  line  cb 
and  acts  in  the  direction  from  c  to  b,  and  the  other  by  the  line 
be  and  acts  in  the  direction  from  b  to  e\  these  components  and: 
the  whole  force  being  to  one  another  as  the  sides  of  the  triangle 
representing  them.  Denoting  the  component  of  the  force  of 
gravity  represented  by  be  by  ft  that  of  the  whole  force,  as  we 
have  seen  in  §9,  being  represented  by  gm,  we  have  sensibly,  put- 
ting be  =  ec,  f :  gm  =  be  :  be.  But  the  angles  at  a  and  c  being 
equal,  as  is  pretty  evident  without  rigorous  demonstration,  the 
lines  forming  the  angles  must  separate  from  each  other  4n  pro- 
portion to  the  distances  from  the  angles,  and  hence  we  have 


50    MOTIONS   OF  BODIES  RELATIVE    TO  EARTH'S   SURFACE. 

de  :  ad  =  be  :  be.  These  ratios  are  also  derived  more  directly 
from  the  well-known  geometrical  relations  of  similar  triangles. 
Putting  the  ratios  above,  which  are  both  equal  to  the  ratio 
be  :  be,  equal  to  each  other,  we  get  fi  gm  =  de  :  ad',  or  represent- 
ing, as  above,  this  latter  ratio  be  e,  we  get  f  \gm-=.ey  orf=. 
egm.  Strictly,  this  expression  of  f  here  is  the  horizontal  com- 
ponent of  the  force  down  the  slope,  but  in  putting  be  =  ec 


Fig.  2. 

above  we  neglect  the  very  small  difference  between  the  two 
where  the  gradients  are  so  small. 

Where  the  gradient  is  very  small,  as  it  usually  is,  the  centrif- 
ugal force  in  the  direction  of  the  slope  is  sensibly  the  same  as 
in  a  horizontal  direction  ;  and  so,  in  order  that  the  centrifugal 
and  centripetal  forces  on  the  slope  may  be  exactly  equal,  the 
gyratory  velocity  must  be  such  as  to  satisfy  the  condition 

w* 
eg=  —  =  rn\ 

as  is  readily  seen  by  comparing  the  expression  of  the  centrip- 
etal force  above,  with  that  of  the  centrifugal  force  Fc  in  §  36. 
Since  g  may  be  regarded  as  constant,  it  is  seen  from  this  ex- 
pression that  the  gradient  of  the  slope  which  satisfies  this  con- 
dition varies  directly  as  the  square  of  the  gyratory  velocity  and 
inversely  as  the  distance  r  of  the  body  from  the  centre  of  gyra- 
tion. With  the  same  value  ofj  w  it  is  seen  that  the  gradient 
very  near  the  centre,  where  r  is  small,  would  be  very  steep,  and 
consequently  this  expression  would  not  hold  there,  since  it  has 


CENTRIFUGAL   FORCE.  $1 

been  assumed  above  that  the  gradient  is  so  small  that  the 
horizontal  and  inclined  distances  do  not  differ  sensibly. 

From  what  precedes,  if  the  railroad  car,  in  the  example 
which  we  have  just  had,  were  to  move  around  upon  a  surface 
declining  at  all  points  toward  the  centre  of  curvature,  or,  what 
would  be  the  same,  if  the  outer  rail  were  a  little  above  the  level 
of  the  inner  one,  then  the  centrifugal  and  centripetal  tendencies 
would  exactly  counteract  each  other,  and  there  would  be  no 
lateral  pressure  against  the  rails,  if  the  gradient  between  the 
two  rails  were  determined  by  the  preceding  expression.  In  the 
•example  above,  the  outer  rail  would  have  to  be  higher  than  the 
inner  one  by  the  ^5-  part  of  the  width  between  them.  Since 
the  required  gradient  differs  with  different  velocities,  the  best 
that  can  be  done  is  to  adapt  the  gradient  to  an  average  velocity, 
or  rather,  to  an  average  of  the  squares  of  the  usual  varying 
velocities. 

Upon  the  same  principle,  the  gradient  between  the  two 
banks  of  a  river,  flowing  in  a  channel  around  a  centre  of  curva- 
ture, can  be  determined.  If  the  velocity  were  2  meters  per 
second  (4.5  miles  per  hour),  and  the  radius  of  curvature  1000 
•meters,  then  the  value  of  the  gradient  e  from  the  preceding  ex- 
pression would  be  22  :  (1000  X  9.806)  —  .000408 ;  and  hence  the 
-level  of  the  water  on  the  opposite  side  from  the  centre  of  curva- 
ture would  be  higher  than  on  the  other  side  the  ^Vo-  part, 
nearly,  of  the  width  of  the  river,  if  all  parts  had  the  same  veloc- 
ity and  the  same  radius  of  curvature. 

39.  If  a  body,  as  at  a,  Fig.  I,  is  at  rest  relative  to  the  sur- 
iace,  with  a  descending  gradient  from  all  sides  toward  the 
•centre  0,  and  the  whole  sub-stratum  of  the  surface  gyrates 
around  this  centre  with  a  velocity  w  at  the  distance  r  from  the 
centre,  it  is  evident  that  the  centrifugal  force  Fc  and  the  coun- 
teracting component  of  gravity  /  along  the  descending  gradient, 
are  precisely  the  same  as  if  the  body  gyrated  with  the  same 
.angular  velocity  around  the  centre  of  gyration,  and  moves  with- 
out friction  over  the  surface,  since  the  absolute  motion  of  the 
body  is  the  same  in  both  cases.  In  order,  therefore,  that  the 
ibody  may  remain  at  rest  upon  such  a  revolving  surface  and  not 


52     MOTIONS   OF  BODIES  RELATIVE    TO   EARTH'S  SURFACE. 


move  either  from  or  toward  the  centre,  the  condition  of  the  ex- 
pression in  §  38  must  be  satisfied.  It  is  seen  from  this  expres- 
sion, since  n  is  constant  with  the  same  angular  velocity  of 
gyration,  that  the  gradient  e  must  be  proportional  to  r,  and 
consequently  vanish  at  the  centre  where  r  vanishes  and  increase 
as  the  distance  r  increases.  Such  a  gradient  would  be  found 
in  a  concave  surface  corresponding  to  a  small  segment  of  a 
spherical  shell,  a  section  of  which,  aob,  in  which  o  is  the  centre, 
is  represented  in  Fig.  3. 

If  the  whole  gyrating  stratum  were  covered  by  a  fluid,  con- 
fined within  a  given  area  by  a  circular  rim,  as  in  the  case  of  a 
very  shallow  basin  of  water  revolving  horizontally  around  its, 
centre,  then  all  parts  of  the  surface  of  the  fluid  in  static  equilib- 
rium and  at  rest  relatively  to  the  basin,  must  have  a  gradient 


d 


Fig.  3. 


satisfying  the  preceding  condition,  and  be  such  as  that  repre- 
sented in  Fig.  3,  in  which  a  body  at  rest  upon  any  part  of  it 
would  not  move  either  toward  or  from  the  centre. 

40.  If  we  now  suppose  the  concave  surface  of  the  revolving 
solid  stratum,  abed,  Fig.  3,  to  be  the  same  as  that  which  a  liquid 
at  rest  relative  to  the  solid  would  assume,  and  that  a  body 
placed  upon  this  surface  has  a  gyratory  velocity  v,  either  in  the 
same  or  the  contrary  direction,  the  surface  gyrating  with  the 
velocity  GJ  at  the  distance  r  of  this  body  from  the  centre  of 
gyration,  then  the  absolute  gyratory  velocity  of  the  body  at  the 
distance  of  r  is  GJ  -|-  v,  the  latter  being  negative  when  the  body 
gyrates  in  the  contrary  way  to  that  of  the  solid.  Hence,  in 
order  to  obtain  now  an  expression  of  the  centrifugal  force  Fc , 
we  must  put  in  the  expression  of  Fc  in  § 36,  oo-\-  ^instead  of  w~ 
But  since  the  square  of  the  sum  or  difference  of  two  quantities, 
or  of  numbers  representing  them,  is  equal  to  the  square  of  the 


CENTRIFUGAL  FORCE.  53 

first,  plus  or  minus  twice  the  product  of  the  first  into  the  sec- 
ond, plus  the  square  of  the  second,  as  any  one  not  familiar  with 
algebraical  operations  can  easily  verify  in  special  numerical 
cases,  we  shall  now  have  for  the  expression  of  the  centrifugal 
force 

,-,  (GO  +  Vf  60'  +  2GOV  +  V* 

Fc  =  ^ ! — J-m  = ! 3 m. 


The  first  term  of  this  expression  <&*m/r  is  the  part  of  the 
centrifugal  force  which  exactly  counteracts  the  tendency  of  the 
body  to  slide  down  the  slope  toward  the  centre  of  concavity 
and  of  gyration,  since  we  have  assumed  that  the  gradient  of  the 
surface  is  such  as  to  satisfy  the  condition  of  §  38,  and  conse- 
quently such  as  a  liquid  surface  would  assume  where  all  parts 
have  the  same  angular  velocity  of  gyration.  The  second  part 
of  this  expression,  containing  both  GO  and  v  as  factors,  depends 
upon  both  GO  and  v,  and  vanishes  if  either  GO  or  v  is  equal  to  o. 
If  v  is  the  velocity  of  gyration  in  the  same  direction  as  that  of 
GO,  then  the  effect  of  this  term  is  positive,  and  the  part  of  the 
force  represented  by  it  tends  to  drive  the  body  away  from  the 
centre  of  the  slope,  being  so  much  force  in  addition  to  that 
which  is  just  sufficient  to  support  the  body  upon  the  slope  and 
to  keep  it  from  sliding  down  toward  the  centre.  But  if  v  is 
negative,  that  is,  contrary  to  the  direction  of  GO,  then  the  cen- 
trifugal force  is  diminished,  and  is  not  sufficient  to  counteract 
the  tendency  of  the  body  to  slide  down  the  inclined  surface 
toward  the  centre.  The  effect  of  this  term,  therefore,  is  to 
deflect  the  body  on  the  concave  surface,  away  from  the  centre 
when  v  is  positive,  but  toward  the  centre  when  negative,  and 
in  both  cases  to  the  right  of  the  direction  of  the  relative  mo- 
tion. The  last  term  in  the  expression  of  Fc,  depending  upon 
7'2,  is  simply  the  centrifugal  force  belonging  to  the  relative  gyra- 
tory velocity,  in  case  the  solid  surface  had  no  gyratory  velocity 
oo.  Consequently  the  effect  of  this  part  of  the  force  is  always 
to  drive  the  body  from  the  centre,  whether  v  is  positive  or 
negative. 


54    MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S    SURFACE. 


On  a  gyrating  surface,  therefore,  in  which  the  condition  of 
§  38  is  satisfied,  namely,  that  the  body  when  at  rest  has  no  ten- 
dency to  move  either  toward  or  from  the  centre,  the  gradient 
and  the  gyratory  velocity  being  such  that  these  two  tendencies 
exactly  counteract  each  other,  we  then  have  for  the  expression 
of  the  effective  centrifugal  force 


m. 


THE  PRINCIPLE  OF  THE  PRESERVATION   OF  AREAS. 

41.  If  a  body  has  a  gyratory  motion  around  any  given 
centre,  and  is  also  acted  upon  by  a  force  in  a  direction  either 
toward  or  from  that  centre,  the  variable  line  connecting  the  body 
with  the  centre,  called  the  radius  vector,  always  sweeps  over 

equal  areas  in  equal  times.  Thus,, 
if  a  body  at#  in  the  annexed  figure 
has  a  gyratory  component  of  velo- 
city from  left  to  right  around  the 
centre  at  o,  and  is  at  the  same 
time  acted  upon  by  a  centripetal 
force  of  any  kind,  so  as  to  cause 
it  to  move,  in  successive  equal  in- 
tervals of  time,  to  the  points  b, 
c,  and  d,  then  the  areas  aob,  boc, 
cod,  etc.,  are  equal.  This  was 
demonstrated  by  Newton,  and  is  a 
firmly  established  principle  in  me- 
chanics. This  equality  of  areas,, 
of  course,  holds  for  each  area,  in 
any  part  of  the  path  of  the  body, 
swept  over  by  the  radius  vector 
in  an  infinitely  small  portion  of  time,  and  these  areas  are 
equal  to  one  half  of  the  product  of  the  radius  vector  into- 
the  component  of  motion  in  this  infinitely  small  portion  of  time 
which  is  perpendicular  to  the  radius  vector,  called  the  gyratory 


Fig.  4. 


THE  PRINCIPLE   OF   THE  PRESERVATION  OF  AREAS.      55 

component  of  motion.  It  also  holds  where  the  body  recedes 
from  the  centre  in  consequence  of  either  the  centrifugal  force 
arising  from  the  gyratory  component  of  motion,  or  any  real 
force  acting  in  a  direction  from  the  centre. 

The  velocity  of  a  body  of  variable  motion  at  any  point  is 
the  space  it  would  pass  over  in  a  unit  of  time,  as  one  second, 
if  the  rate  of  motion  which  it  has  at  that  point  should  con- 
tinue through  that  time,  and  not  the  space  which  it  actually 
passes  over  in  a  unit  of  time  with  varying  velocity.  The  gyra- 
tory component  of  velocity  is  that  part  of  its  actual  velocity  in 
the  path  described,  resolved  in  a  direction  perpendicular  to  the 
radius  vector.  For  instance,  if  the  body  at  d  in  the  figure 
above  has  a  rate  of  motion  which,  if  unchanged,  would  carry 
it  to  e  in  the  direction  of  the  tangent  in  a  unit  of  time,  then  if 
this  velocity  de  is  resolved  into  the  two  components  ei  and  di, 
the  former  is  called  the  gyratory  and  the  latter  the  centripetal 
velocity.  As  the  velocities  depend  upon  the  rate  of  motions 
at  any  given  point,  and  not  upon  the  actual  motion  in  a  unit  of 
time,  and  the  areas  swept  over  in  infinitely  small  portions  of 
time  are  equal  to  half  the  product  of  the  radii  vectores  into  the 
gyratory  components  of  motion,  and  these  areas  are  all  equal, 
it  is  evident  that  the  gyratory  velocities  of  the  body  in  different 
parts  of  its  orbit  are  inversely  as  the  radii  vectores.  Putting, 
therefore,  as  heretofore,  w  for  the  gyratory  velocity  and  r  for 
the  radius  vector,  or  variable  radius,  we  have  for  all  parts  of 
the  path  of  motion 

rw  =  c, 

In  which  c  is  a  constant.  This  is  the  expression  of  the  law  of 
equal  areas  in  this  case.  Hence  the  nearer  the  body  comes  to 
the  centre  the  greater  is  the  gyratory  velocity,  and  vice  versa. 

A  familiar  example  of  this  law  is  observed  in  twirling  a  small 
body  attached  to  the  end  of  a  string  around  the  end  of  a  stick, 
and,  after  the  gyratory  motion  has  been  established,  allowing 
the  string  to  wind  up  around  it.  The  string  acts  as  a  force, 
continually  drawing  the  body  closer  to  the  axis  or  centre  of 


56     MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S   SURFACE. 

gyration,  and  as  this  is  done  the  gyratory  velocity  increases, 
and  when  the  string  becomes  very  short  the  velocity  becomes 
very  great.  Just  the  reverse  takes  place  if  the  motion  is  such 
as  to  unwind  the  string,  and  to  allow  the  body  to  recede  to 
greater  distances  from  the  centre  of  gyration.  As  the  dis- 
tance increases,  the  gyratory  velocity  becomes  less  ;  and  when 
the  distance  becomes  very  great,  the  gyratory  velocity  becomes 
very  small. 

A  more  perfect  exemplification  of  this  law  is  found  in  the 
motions  of  the  planets  and  comets  in  their  orbits  around  the 
sun.  In  this  case  the  law  of  the  centripetal  attractive  force  is 
such  as  to  cause  elliptical  orbits ;  but  the  law  holds,  whatever 
may  be  the  law  of  this  force  and  the  path  of  the  body.  At 
aphelion,  where  the  planet  or  comet  is  at  its  greatest  distance, 
the  gyratory  velocity  is  least  ;  but  as  it  comes  nearer  to  the 
sun  in  moving  around  to  its  perihelion,  the  gyratory  velocity 
increases  in  accordance  with  the  law  above,  except  so  far  as  it 
may  be  slightly  affected  by  the  perturbations  of  the  other 
planets.  In  the  case  of  comets  with  very  eccentric  elliptical 
orbits,  the  radius  vector  at  perihelion  becomes  very  small,  and 
the  corresponding  gyratory  velocity  enormous. 

42.  As  the  body  is  drawn  or  forced  toward  the  centre  of 
gyration,  the  gyratory  velocity,  if  the  body  is  free,  is  increased, 
just  as  in  the  case  of  a  force  acting  upon  a  body  in  the 
direction  of  its  motion,  and  the  amount  of  acceleration  in  a 
unit  of  time,  multiplied  into  its  mass,  in  the  former  case  as  in 
the  latter,  is  the  measure  of  the  force  causing  the  acceleration. 
If  the  body  is  constrained  to  move  in  a  given  path,  not  directly 
toward  the  centre,  or  is  retarded  by  frictional  or  other  resist- 
ances, a  part  of  this  force  may  be  spent  in  causing  pressure 
and  overcoming  the  resistance  of  the  friction,  and  the  balance 
only,  in  causing  acceleration  in  the  direction  of  motion. 

According  to  the  preceding  expression  of  the  law  of  equal 
areas,  rw  =  c,  if  r  is  decreased  by  the  action  of  any  kind  of  cen- 
tripetal force  by  the  \/m  part  of  r  in  a  very,  strictly  infinitely, 
small  portion  of  time,  m  being  a  very  large  or  infinitely  great 
number,  then  w  is  increased  by  the  same  part,  that  is,  by 


THE   PRINCIPLE   OF    THE   PRESERVATION  OF  AREAS.      $? 

i/m  part  of  w,  or  w/m.  If  we  now  suppose  that  r  continues 
to  decrease  by  the  same  rate  during  a  unit  of  time,  and  we  call 
this  rate,  or  centripetal  velocity  of  the  body,  x,  then  r  is 
changing  at  the  rate  of  the  xj ' r  part  of  it  in  a  unit  of  time; 
and  consequently  w,  if  it  increased  uniformly,  would  increase 
the  x/r  part  of  w  or  xw/r  in  a  unit  of  time.  Now  the  in- 
crease of  velocity  in  a  unit  of  time  is  called  the  acceleration, 
and  the  acceleration  multiplied  into  the  mass  m  is  the  measure 
of  the  force  which  causes  the  acceleration.  And  this  force 
acting  in  the  direction  of  the  gyratory  velocity  w,  and  so  at 
right  angles  to  the  radius,  may  be  called  the  gyratory  force. 
Putting,  therefore,  Fg  for  this  force,  we  have 


xw 

— 

r 


The  gyratory  force,  therefore,  is  directly  as  the  product  of 
the  gyratory  velocity  w  into  the  centripetal  velocity  x,  and  in- 
versely as  the  distance  r  of  the  body  from  the  centre.  If  r, 
therefore,  could  become  infinitely  small,  the  gyratory  force 
would  become  infinitely  great.  By  comparing  this  expression 
with  that  of  the  centrifugal  force  Fe ,  §  36,  it  is  seen  that  they 
are  both  equal  where  x  and  w  are  equal,  that  is,  where  the 
velocity  of  the  body  toward  the  centre  is  equal  to  the  gyratory 
velocity. 

43.  If  we  suppose  that  a  horizontal  plane  has  a  gyratory 
motion  around  the  centre  o  in  Fig.  5  (p.  58)  with  a  velocity 
ab  at  the  distance  of  a  from  the  centre,  the  line  AB  being  sup- 
posed to  be  fixed  in  space,  and  also  that  a  body  at  a,  while 
acted  upon  by  a  centripetal  force  toward  o,  also  has  a  gyratory 
velocity  relative  to  the  plane  equal  to  be,  then  the  absolute 
gyratory  velocity  is  ac.  Denoting  now,  as  in  §  40,  by  GJ 
the  gyratory  velocity  ab  of  the  plane  at  the  distance  of  oa  or 
r,  and  by  v  the  gyratory  velocity  be  relative  to  the  plane,  then 
the  absolute  gyratory  velocity  ac  of  the  body  is  GO  -f  v,  and 
Whence  in  this  case,  in  order  to  get  the  gyratory  force  Fft  we 


58     MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S   SURFACE.. 

must  put  co  +  v  for  w  in  the  preceding  expression,  and  we  thus- 
get 

r,  XGO  .    XV  N   X 

r.  = in  A m-=.   GO-T-V)  —m. 

r  r  J  r 

But  the  gyratory  velocity,  reckoned  from  the  line  ob  instead 
of  the  fixed  line  AB  in  space,  is  greater  by  the  difference. 


between  ab  and  a'b' ,  supposing  the  body  to  move  with  uniform 
velocity  toward  the  centre  by  the  distance  aa!  in  a  unit  of  time. 
Now  in  a  unit  of  time  under  these  conditions  ab  is  greater  than 
a'b'  by  the  x/r  part  of  c»,  or  xco/r.  Hence  if  the  gyratory  veloci- 
ty is  reckoned  from  the  line  ob  instead  of  the  fixed  line  AB,  we 
must  add  xco/r  to  the  acceleration  where  the  gyratory  velocity 
is  reckoned  from  the  gyrating  line  ob  fixed  relatively  to  the 
plane,  but  not  in  space.  With  this  additional  term  added  to 
the  acceleration  in  the  previous  case,  we  get  for  the  relative 
gyratory  force 

~  2XG>)  .     XV  .   X 

Fg.  =  m  -\ m  =  (2Go  +  v)  —  m. 

r  r  }  r 


CENTRIFUGAL   FORCE   OX    THE  EARTH'S  SURFACE.       59 

By  comparing  this  expression  with  the  last  expression  of  the? 
centrifugal  force  Fe  in  §  40,  it  is  seen  that  they  are  the  same  if 
x  and  v  are  equal,  that  is,  if  the  centripetal  velocity  is  equal  to- 
the  relative  gyratory  velocity.  From  this  it  is  to  be  understood 
that,  if  a  body  has  a  gyratory  velocity  relative  to  a  gyrating 
surface  around  the  same  centre,  in  which  the  condition  of  §40- 
is  satisfied,  and  the  gyrating  body  is  drawn  in  toward  the  centre 
by  a  centripetal  force  of  any  kind,  with  a  given  velocity,  there 
results  a  gyratory  force  which  tends  to  overcome  resistances  to> 
gyratory  motion  on  the  surface,  or  the  inertia  of  the  body, 
when  there  are  no  frictional  or  other  resistances,  and  to  cause 
accelerated  gyratory  velocity,  and  that  this  force  is  exactly 
equal  to  that  which  tends  to  drive  the  body  away  from  the 
centre  when  the  gyratory  velocity  is  equal  to  the  centripetal 
velocity  in  the  other  case.  If  the  force  is  centrifugal  instead 
of  centripetal,  then  the  direction  of  the  gyratory  force  is  re- 
versed, and  the  relative  greater  velocity  is  diminished  and  may 
be  even  overcome  and  reversed  as  the  distance  of  the  body 
from  the  centre  is  increased ;  just  as  has  been  shown,  §40,  in 
the  other  case  when  the  gyratory  velocity  v  is  negative,  or  in 
the  contrary  direction,  the  deflecting  force  tends  to  draw  the 
body  from  the  direction  of  motion  toward  instead  of  from  the 
centre. 

If  the  body  is  not  free  to  gyrate  relatively  to  the  gyrating 
surface,  but  is  constrained  to  move  either  directly  towards  or 
from  the  centre,  as  in  a  groove,  then  the  gyratory  force  causes 
pressure  against  the  one  side  or  the  other,  according  as  the 
body  is  forced  toward  or  from  the  centre. 

CENTRIFUGAL  FORCE  IN  MOTIONS   ON  THE   EARTH'S  SURFACE.. 

44.  With  the  preceding  preliminary  results  with  regard  to- 
centrifugal  force  in  general,  §§35—40,  we  are  now  prepared  to 
investigate  the  effect  of  the  centrifugal  force  arising  from  the 
earth's  rotation  on  its  axis,  upon  the  motions  of  bodies  upon; 
its  surface.  Let  PCE,  Fig.  6  (p.  60),  represent  one  quadrant  of  a. 


*5O    MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACE. 

meridional  section  of  the  earth  turning  on  its  axis,  of  which  P 
is  the  pole,  C  the  centre,  and  E  the  point  in  the  equator  inter- 
sected by  this  plane,  and  let  a  be  a  body  at  rest  on  the  earth's 
surface,  subject  to  the  action  of  the  centrifugal  force  arising 
from  the  earth's  rotation  and  the  consequent  gyration  of  the 
body  around  the  point  e  as  a  centre  in  the  semi-axis  PC.  The 
amount  of  this  force  is  given  by  the  expression  of  F,  in  §  36, 
and  it  is  in  the  direction  of  the  line  ab  in  the  plane  of  gyration, 
and  the  body  would  be  driven  away  in  this  direction  if  this 
centrifugal  force  were  not  counteracted  by  the  stronger  force 


A 


of  the  earth's  attraction.  Let  us  now  suppose  that  the  centrifu- 
gal force  is  represented  by  the  line  ab,  and  that  this  is  resolved 
into  two  component  forces  in  the  directions  of  ad  and  ac,  the 
former  parallel  and  the  latter  perpendicular  to  the  earth's  sur- 
face, which  together  are  equivalent  to  the  force  represented  by 
ab.  If  the  points  c  and  d  are  determined  by  perpendiculars 
drawn  to  these  lines  from  the  point  b,  thus  completing  the 
parallelogram  of  forces,  it  is  well  known  that  the  original  or 
resultant  force,  and  the  two  components  in  the  directions  of 
•ad  and  ac,  are  respectively  proportional  to  the  lines  ab,  ad, 
and  ac. 

The  component  of  the  centrifugal  force  acting  in  the  direc- 
tion of  ad,  and  represented  by  this  line,  tends  to  drive  the  body 


CENTRIFUGAL  FORCE   ON   THE  EARTH'S  SURFACE.         6*. 

on  the  earth's  surface  from  the  pole  toward  the  equator,  and  if 
the  surface  were  perfectly  smooth  and  without  friction,  would 
do  so  on  a  spherical  globe  ;  but  this  tendency  is  exactly  counter- 
acted by  the  tendency  to  slide  down  the  ellipsoidal  surface  of 
the  earth  toward  the  pole  P.  The  ellipticity  of  the  rotating" 
earth  is  necessarily  such  that  these  two  tendencies  or  forces  are 
exactly  balanced,  and  just  as  in  the  case  of  the  concave  gyrat- 
ing surface  in  §  39,  the  concavity,  and  gradient  of  the  slope  at 
each  point,  are  such  that  the  tendency  to  slide  down  toward 
the  centre  is  exactly  counteracted  by  the  centrifugal  force.  In 
fact  the  earth's  surface  of  either  hemisphere,  referred  to  a 
spherical  surface,  or  even  one  everywhere  normal  to  the  direc- 
tion of  the  earth's  attraction,  is  a  concave  surface,  lower  at  the 
pole  than  at  the  equator.  A  body,  therefore,  at  rest  upon  the 
ellipsoidal  surface  has  no  tendency  to  move,  either  toward  the 
equator  on  account  of  one  component  of  the  centrifugal  force, 
or  toward  the  pole  on  account  of  the  earth's  ellipticity. 

The  other  component  of  the  centrifugal  force,  acting  in  the 
direction  of,  and  represented  by,  ac,  tends  simply  to  counteract 
a  comparatively  small  part  of  the  force  of  the  earth's  attraction, 
thus  causing  the  force  of  gravity  to  be  a  little  less  than  that  of 
the  earth's  attraction. 

45.  The  centrifugal  force  of  the  earth's  rotation  acting  in 
the  plane  of  gyration  is,  by  the  first  form  of  the  expression  o£ 
Fc  in  §  36, 

Fc  —  rn*m, 

in  which  r  corresponds  to  ae  in  the  figure,  and  in  which  n  is  the 
gyratory  velocity  of  the  earth's  rotation  in  terms  of  the  radius. 
This  being  a  constant,  this  force  is  proportional  to  r,  and  this 
latter  is  proportional  to  the  cosine  of  the  latitude  if  we  neglect, 
as  we  may  in  researches  of  this  kind,  quantities  of  the  order  of 
the  earth's  ellipticity.*  Putting,  therefore,  /  for  the  latitude 

*  Neglecting  such  quantities,  the  line  ao,  Fig.  6,  can  always  be  taken  as  the 
mean  radius  r ',  and  may  be  supposed  to  be  drawn  to  the  centre  C  instead  of  0, 
and  so  perpendicular  to  the  surface  at  a.  Then  the  angle  aCE  =  CaE  is  the 
latitude  of  the  body  at  a,  and  we  consequently  have  r  \r  =  I  :  cos  /,  or  r  =  r 
cos  /.  And  as  r  is  constant,  we  have  r  =  cos  /  when  r  is  taken  as  unity. 


'62     MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACE. 

and  r'  for  the  mean  radius  of  the  earth,  we  have  r  •=.  r'  cos  /, 
and  hence  the  preceding  expression  becomes 

Fc  =  r'ri*  cos/  m. 

The  cosines  for  each  fifth  degree  of  latitude  are  given  in 
Table  V,  to  which  those  who  are  not  familiar  with  such  func- 
tions can  refer,  and  from  which  it  is  seen  that  they  are  great- 
est at  the  equator  and  vanish  at  the  poles.  The  horizontal 
component  of  the  centrifugal  force,  represented  by  ad  in  the 
figure,  varies  on  the  different  latitudes  in  comparison  with  the 
whole,  as  the  sines  of  the  latitudes.  These  also  are  given  in 
Table  V,  from  which  it  is  seen  that  this  component,  in  com- 
parison with  the  whole,  is  greatest  at  the  pole  and  vanishes  at 
the  equator.  But  as  the  whole  varies  as  the  cosines  of  the  lati- 
tudes, the  horizontal  component  varies  as  the  product  of  the 
cosine  into  the  sine.  Putting,  therefore,  Fh  for  the  horizontal 
component  of  the  centrifugal  force,  we  have 

Fh  —  r'n*  cos/  sin/  m. 

This  component,  therefore,  vanishes  both   at  the  equator  and 
the  pole,  and  is  a  maximum  on  the  parallel  of  45°*. 

Since  the  earth  performs  a  complete  sidereal  revolution  on 
its  axis  in  2$h.  56m.  45.,  or  86,164  seconds,  any  part  of  the 
earth,  at  the  distance  of  unity  from  the  axis,  moves  through  the 
space  27t  =  6.2832  such  units  in  this  time.  Hence  the  space 
moved  through  in  one  second,  in  terms  of  the  radius,  is 
6.2832/86164  =  0.00007292,  which  is  the  value  of  n  above.  The 
equatorial  radius  of  the  earth  being  6,378,190  meters,  we  get 
for  the  acceleration  of  the  centrifugal  force  at  the  equator,  in 
meters,  or,  in  other  words,  the  force  for  unity  of  mass,  r'n*  = 
6,378,190  X  (o.oooo7292)2  =  0.033913.  Comparing  this  with 

*  By  a  well-known  transformation  we  can  put  cos  /sin  1=  -J  sin  2/.  On  the 
parallel  of  45°  we  have  2/  =  90°,  and  hence  the  maximum  is  on  that  parallel  as 
stated. 


CENTRIFUGAL   FORCE   ON   THE   EARTH'S  SURFACE.          63 

the  acceleration  of  the  force  of  standard  gravity,  which  is 
9.806  m.,  we  get  0.033913  : 9.806  =  1/289,  very  nearly. 

The  velocity  of  rotation  of  any  point  on  the  earth's  surface 
is  rn  =  r'n  cos  /,  since  n  is  simply  the  ratio  between  this  velocity 
aijd  the  radius  of  gyration  r.  These  values,  and  also  the  values 
of  r,  corrected  for  the  effect  of  the  earth's  eccentricity,  are 
given  for  each  degree  of  latitude  in  Table  V. 

Since  the  centrifugal  force  is  as  the  square  of  n,  if  the  gyra- 
tory velocity  of  rotation  were  seventeen  times  greater,  the  cen- 
trifugal force  at  the  equator  would  be  very  nearly  equal  to  that 
of  the  earth's  attraction,  since  the  square  of  17  is  equal  to  289, 
and  then  a  body  at  the  equator  would  have  little  or  no  pressure 
upon  the  earth's  surface ;  and  if  the  rotary  velocity  were  still  a 
little  more  increased,  the  body  would  fly  off  into  space, — not, 
however,  in  the  direction  of  a  tangent,  as  is  often  said,  but  in 
an  elliptic  orbit,  which  would  bring  it  back  again  to  the  earth's 
surface. 

46.  If  a  body  at  a,  Fig.  6,  has,  in  addition  to  the  gyratory 
east  velocity  due  to  the  earth's  rotation,  also  an  easterly* 
velocity  relative  to  the  earth's  surface,  called  relative  velocity, 
the  absolute  east  velocity  is  then  increased  by  the  east  com- 
ponent of  this  velocity,  and  the  centrifugal  force  in  the  plane 
of  gyration  is  increased  in  proportion  to  the  square  of  the 
absolute  east  velocity.  The  centrifugal  force  is  then  given  by 
the  first  form  of  the  expression  of  Fe ,  in  §  40,  using  for  GO  and  r, 
for  any  given  latitude,  the  values  in  Table  V.  But  the  hori- 
zontal component  of  this  force,  the  part  which  tends  to  drive 
the  body  from  the  pole  toward  the  equator,  we  have  seen,  is  to 
the  whole  as  the  sine  of  the  latitude  to  unity;  and  hence  in 
order  to  obtain  the  expression  for  the  horizontal  component 
Fh  in  this  more  general  case,  in  which  the  body  has  an  east  or 

*  In  this  work  east  or  eastern  is  used  in  an  exact  sense,  so  that  an  east 
or  eastern  direction  means  one  exactly  toward  the  east,  while  easterly  is  used 
more  vaguely  to  indicate  directions  varying  considerably  from  an  exact  eastern 
direction,  but  having  a  large  east  component.  An  east  wind  is  one  coming  ex- 
actly from  the  east,  while  an  easterly  one  may  have  a  considerable  north  or 
south  component  of  motion.  So  for  all  other  points  of  the  compass. 


64     MOTIONS  OF  BODIES   RELATIVE    TO  EARTH'S  SURFACED 

west  relative  velocity  v  in  addition  to  that  of  the  earth's  rota- 
tion, we  must  multiply  the  expression  of  Fc ,  in  §  40,  into  sin  /, 
and  we  thus  get 

ft/   +  200V  +  V*      . 

F  = ! sin  /  m.  • 


The  first  term  in  this  expression  (oo*/r)  sin  lm  —  rn*  sin  Im 
=  r'n*  cos  /  sin  Im,  putting  r  —  r'  cos  /  to  obtain  the  last  form, 
is  the  part  of  the  horizontal  component  of  the  centrifugal  force, 
as  shown  in  the  last  section,  which  is  exactly  counteracted  by 
the  tendency  of  the  body  to  slide  down  the  elliptical  surface 
toward  the  pole,  so  that  in  the  case  of  a  body  resting  upon  such 
a  surface,  and  having  an  easterly  relative  velocity  with  an  east 
component  v,  the  force  which  tends  to  drive  it  toward  the 
equator  is  expressed  by  the  last  two  terms  above  ;  so  that  we 
get  in  this  case,  putting  Fv  for  the  force  deflecting  to  the  right 
or  south  of  the  direction  of  motion  of  the  east  component  of 
velocity  v, 

i> 
Fv  =.  (200  -f-  v)  —  sin  /  m. 

This  is  the  same  as  would  be  obtained  by  multiplying  the  last 
expression  of  Fc ,  in  §  40,  into  sin  /. 

If  the  relative  velocity  is  westerly,  then  the  west  component 
v  is  negative ;  and  the  absolute  velocity  of  gyration,  and  conse- 
quently the  centrifugal  force  and  its  horizontal  component,  are 
less  than  in  the  case  in  which  the  body  is  at  rest  on  the  earth's 
surface,  and  in  which  case  v  =  o.  This  force,  therefore,  in  this 
case,  is  not  sufficient  to  counteract  completely  the  tendency  of 
the  body  to  move  on  the  ellipsoidal  surface  toward  the  pole, 
and  there  is  a  residual  part  of  this  tendency  or  force  left,  equal 
to  the  preceding  expression  where  v  is,  negative,  and  the  body 
consequently  tends  to  move  toward  the  pole.  If,  therefore,  the 
body  has  a  relative  motion  with  an  east  component  of  motion, 
'  it  is  deflected  toward  the  equator  ;  but  if  it  has  a  relative  motion 


THE  PRINCIPLE   OF  EQUAL  AREAS.  65 

with  a  west  component  of  motion,  it  is  deflected  toward  the 
pole ;  and  consequently  in  both  cases  to  the  right  of  the  direc- 
tion of  the  east  or  west  component  of  motion  in  the  northern 
hemisphere,  and  the  contrary  in  the  southern,  where  sin  /  is 
negative. 

If  the  earth  had  no  rotation  on  its  axis  and  the  body  had  an 
east  or  west  component  of  velocity  z>,  we  should  still  have  the 
last  term  in  the  preceding  expression  of  Fh ,  depending  upon  ^2, 
which  is  independent  of  GO,  the  earth's  gyratory  velocity,  and  is 
the  same  as  if  the  body  had  an  absolute  east  or  west  velocity 
equal  to  v  upon  the  earth  without  rotation  on  its  axis.  This 
part  of  the  force,  however,  is  generally  very  small  in  all  ordinary 
cases  of  relative  motions  on  the  earth's  surface,  since  the 
velocities  of  these  are  generally  very  small,  in  comparison  with 
the  velocities  of  the  earth's  rotation,  as  given  in  Table  V,  ex- 
cept very  near  the  poles.  For  instance,  on  the  parallel  of  45°, 
where  GO  =  329  meters  per  second,  if  v  had  one  tenth  of  this 
value,  say  33  meters  (about  74  miles  per  hour),  it  is  seen  from 
a  comparison  of  the  two  terms  in  the  preceding  expression  of 
Fv ,  that  the  latter,  which  is  independent  of  GO,  would  be  only 
-fa  part  of  the  other  depending  on  GO.  If  the  relative  gyratory 
velocity  were  west  and  equal  to  twice  the  east  velocity  of  the 
earth's  rotation,  then,  it  is  seen,  the  whole  deflecting  force  Fv 
would  vanish,  since  then  v  would  be  equal  to  200,  and  be 
negative. 


THE   PRINCIPLE   OF  EQUAL  AREAS   IN   MOTIONS  ON   THE 

EARTH'S  SURFACE. 


47.  If  a  free  body  upon  the  spheroidal  surface  of  the  earth, 
supposed  to  be  perfectly  smooth  and  without  friction,  has  an 
absolute  gyratory  velocity  around  the  earth's  axis,  and  is  also 
acted  upon  by  a  force  in  the  plane  of  the  meridian  in  a  direction 
either  directly  toward  or  from  the  pole,  then,  as  the  body  ap- 
proaches or  recedes  from"  the  axis,  the  principle  of  equal  areas 
explained  in  §  41  holds  in  this  case  also,  just  as  it  does  where 


66     MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S    SURFACE. 

the  body  is  forced  directly  toward  or  from  the  centre  of  gyra- 
tion, provided  we  consider  the  motions  of  the  body,  and  the 
areas  swept  over  by  the  radius,  as  projected  upon  a  plane  per- 
pendicular to  the  axis  of  the  earth's  rotation. 

Since  the  perfectly  smooth  surface  of  the  earth  without 
friction  can  have  no  effect  upon  the  absolute  motions  of  the 
body  in  space,  they  are  entirely  independent  of  the  earth's  rota- 
tion, and  are  the  same  as  if  the  earth  were  at  rest.  If  the  body 
on  the  parallel  of  a,  Fig.  6,  has  an  absolute  gyratory  velocity 
along  that  parallel,  either  the  same  as,  or  greater  or  less  than, 
that  of  the  earth's  surface,  and  is  forced  toward  the  pole  until 
it  arrives  at  the  parallel  of  a',  and  the  radius  becomes  a ' e'  in- 
stead of  ae,  the  effect  upon  the  absolute  gyratory  velocity  around 
the  earth's  axis  is  the  same  as  if  the  body  had  been  forced  di- 
rectly in  the  same  plane  from  a  to  z,  and  the  absolute  gyratory 
velocities  on  the  two  parallels  are  inversely  as  the  distances  from 
the  axis.  For  the  force  acting  along  the  earth's  surface  in  the 
plane  of  the  meridian  may  be  resolved  into  two  components,  the 
one  in  a  direction  parallel  to  the  earth's  axis,  and  the  other  perpen- 
dicular to  it,  so  that  the  former  has  no  effect  upon  the  gyratory 
velocity,  and  the  latter  only  is  a  central  force,  directed  toward 
the  earth's  axis  and  the  centre  of  gyration.  The  absolute 
gyratory  velocity,  therefore,  is  determined  by  the  equation  of 
§  41,  rw  =  c,  where  the  value  of  c  is  known.  If  the  values  of 
r  and  w  are  known  for  any  given  latitude,  and  are  denoted  by 
r'  and  w'  respectively,  then  we  have  r'w'  =  c,  and  the  preced- 
ing equation  becomes 

rw  =  r(cj  -\-v)  =  r'w' , 

putting,  as  heretofore,  for  w  the  sum  of  its  two  components  &> 
and  v,  the  former  being  the  gyratory  velocity  of  the  earth's 
surface  and  the  latter  that  of  the  body  relative  to  the  earth's 
surface.  From  this  expression,  with  the  values  of  r'  and  w' 
corresponding  to  any  given  latitude  I',  the  value  of  w,  and  also 
of  v,  are  known  for  any  latitude  /.  For  since  the  values  of  r 


THE  PRINCIPLE   OF  EQUAL   AREAS.  6? 

£or  different  latitudes  are  as  the  cosines  of  these  latitudes,  by 
dividing  each  term  of  the  preceding  equation  by  r,  we  get 


in  which  GO'  and  v'  are  the  values  of  GO  and  v  corresponding  to 
/  =  /'.  The  values  of  the  cosines  and  also  of  GO'  are  given  in 
Table  V. 

48.  The  following  important  applications  may  be  made  of 
the  preceding  principle  by  means  of  this  expression.  If  a  body 
on  the  equator  having  no  relative  east  or  west  velocity  were 
forced  toward  the  pole,  the  value  of  cos  /'  in  this  case  being 
unity,  we  should  have,  by  means  of  the  values  of  GO  and  cos  / 
in  Table  V,  on  the  parallel  of  45°,  where  cos  /  is  equal  to  0.707, 
for  the  value  of  w,  465/0.707  =  658  meters  per  second  ;  on  the 
parallel  of  60°,  where  cos  /=o.5,  the  value  of  w  would  be 
465/0.5  =  930  meters  per  second  ;  on  the  parallel  of  80°,  where 
cos  7=0.174,  we  should  have  2^  =  465/0.174  =  2674  meters 
per  second.  Also,  for  points  much  nearer  the  pole  it  is  seen 
that  w  would  be  still  very  much  greater. 

But  these  are  the  velocities  reckoned  from  a  fixed  plane  in 
space  and  not  from  a  given  meridian  on  the  earth's  surface. 
To  obtain,  therefore,  the  relative  east  velocities,  or  values  of  v, 
we  must  subtract  from  these  the  values  of  GO  in  Table  V,  which 
are  the  absolute  east  or  gyratory  velocities  of  the  earth's  sur- 
face. Hence,  deducting  these  from  the  absolute  velocities 
above,  we  get,  on  the  parallel  of  45°,  ^=658  —  329  =  329 
meters  per  second  ;  on  the  parallel  of  60°,  v  =  930  —  232  =  698 
meters  per  second;  and  on  the  parallel  of  80°,  v  =  2674  —  8  1 
=  2593  meters  per  second. 

If  the  body  before  leaving  the  equator  had  an  east  or  west 
relative  velocity,  then  the  absolute  velocity  here,  w'  ,  would  be 
greater  or  less  by  this  amount,  and  so  the  absolute  velocities  on 
the  several  parallels  above,  from  which  the  values  of  GO  have  to 
be  deducted  in  order  to  obtain  the  relative  values  v,  would  all 
.be  greater  or  less  in  the  same  proportion. 


68    MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACED 

If  the  initial  position  of  the  body  were  that  of  some  par- 
allel between  the  equator  and  the  pole  without  any  initial 
relative  motion,  then,  if  forced  toward  the  pole,  it  would 
gradually  acquire  an  east  component  of  relative  velocity,  which, 
near  the  pole,  would  be  enormously  great,  but  if  forced  from 
the  pole,  it  would  gradually  acquire  a  west  component  of 
velocity  relative  to  the  earth's  surface.  Thus  a  body  without 
any  relative  east  or  west  velocity  on  the  parallel  of  30°,  where 
the  absolute  east  or  gyratory  velocity  of  the  earth's  surface  is- 
403  meters  per  second,  on  arriving  at  the  parallel  of  60°  would 
have  this  velocity  increased  inversely  as  the  cosines  of  the 
latitudes,  that  is,  as  0.500  to  0.866,  and  hence  would  be  698 
meters  per  second,  and  deducting  from  this  the  value  of  GO,  in 
Table  V,  for  this  parallel  we  should  have  a  relative  east  veloc- 
ity v  =  698  —  232  =  466  meters  per  second.  But  if  the  body 
were  forced  directly  toward  the  equator,  on  arriving  there  its 
absolute  east  velocity  would  be  decreased  inversely  as  the 
cosine  of  30  degrees  to  unity  or  as  I  to  0.866,  and  hence  would 
be  349  meters  per  second.  Deducting  this  from  the  absolute 
easterly  velocity  of  the  earth  at  the  equator,  we  get  for  the 
relative  west  component  of  the  velocity  of  the  body  at  the 
equator  465  —  349  =  1 16  meters  per  second. 

If  the  initial  relative  west  component  of  velocity  were 
exactly  equal  to  the  absolute  east  or  gyratory  velocity,  either 
at  the  equator  or  any  parallel  of  latitude,  then  the  initial  abso- 
lute gyratory  velocity  w'  would  be  o,  and  the  body  then  would 
move  in  space  directly  toward  or  from  the  pole,  and  its  relative 
west  velocities,  at  all  latitudes,  would  be  those  of  the  absolute 
east  velocities  of  the  earth's  surface. 

The  preceding  results,  obtained  from  the  principle  of  §  41, 
differ  very  much  from  those  obtained  from  the  principle 
adopted  by  Hadley,  about  the  year  i/35>  m  explaining  the 
trade-winds,  namely,  that  a  body,  being  forced  directly  toward 
or  from  the  pole,  tends  to  keep  its  initial  absolute  gyratory 
velocity.  He  says:7  "  A  particle  of  air  drawn  from  the  tropics, 
where  it  is  supposed  to  have  no  motion  east  or  west,  toward  the 
equator  acquires  a  westward  velocity  on  account  of  the  parallels- 


THE  PRINCIPLE   OF  EQUAL  AREAS.  69 

•continually  enlarging.  The  increase  of  the  parallels  from  the 
tropics  to  the  equator  is  in  the  ratio  of  917  to  1000,  and  hence 
the  westward  motion  in  an  hour  is  83  miles  at  the  equator, 
which  is  decreased  by  the  effect  of  the  earth's  surface  to  what  is 
observed."  But  from  what  has  been  shown  above,  the  velocity 
of  a  body  having  an  absolute  east  velocity  of  917  miles  per  hour 
at  the  tropics,  as  here  supposed,  would  be  decreased  at  the 
equator  in  the  ratio  of  unity  to  the  cosine  of  the  latitude  at 
the  tropics,  or  as  I  to  0.917.  Hence,  instead  of  still  having  an 
absolute  east  velocity  of  917  miles  per  hour,  it  would  have  a 
velocity  of  only  917  x  0.917  =  841  miles  per  hour.  This  being 
deducted  from  1000,  the  supposed  absolute  east  velocity  of  the 
earth's  surface  at  the  equator,  we  have  159  miles  for  the  rela- 
tive west  velocity  there,  instead  of  83  miles  as  given  above. 

According  to  this  erroneous  principle,  in  order  to  obtain  the 
relative  east  components  of  velocity  of  the  body  at  the  several 
latitudes,  in  moving  from  the  equator  to  the  pole  in  the  pre- 
ceding example,  it  would  be  necessary  to  subtract  the  absolute 
east  velocities  of  the  several  parallels,  as  given  in  Table  V, 
from  that  of  the  equator,  and  we  should  thus  get  in  meters  per 
second,  at  the  parallel  of  45°,  v  =  465  —  329  =  136;  at  the 
parallel  of  60°,  v  =  465  —  232  =  233  ;  and  at  the  parallel  of  80°, 
v=  465  —  81  =  384. 

These  differ  very  much  from  the  velocities  obtained  above 
upon  the  correct  principle,  which  is  that  of  equality  of  areas  in 
the  case  of  central  forces. 

49.  The  gyratory  force  Fg  in  this  case — that  is,  the  tendency 
of  the  body,  when  free,  to  acquire  an  east  component  of  ve- 
locity relative  to  the  earth's  surface,  and  when  not  free,  to 
cause  pressure  and  to  overcome  resistances  to  such  relative 
motion — is  the  same  as  in  the  case  of  any  gyrating  surface 
where  the  body  is  forced  toward  the  centre  with  the  velocity 
of  ;tr,  and  is  given  by  the  last  expression  of  Fg  in  §  43.  But 
this  may  be  given  in  a  function  of  the  polar  component  of 
velocity  of  the  body  in  moving  on  the  earth's  surface  instead 
of  a  function  of  x,  which  is  the  velocity,  in  this  case,  with 
which  it  approaches  the  earth's  axis.  From  Fig.  6  it  is  seen 


70    MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACED 

that  by  similar  triangles  we  have  aa!  :  ai=  aC  \  Ce  =  i  :  sin  /r 
neglecting  quantities  of  the  order  of  the  earth's  eccentricity,. 
and  supposing  aa'  to  be  so  small  as  not  to  deviate  sensibly 
from  a  straight  line.  If  we  let  this  represent  the  polar  com- 
ponent of  velocity  of  the  body  on  the  earth's  surface  and 
denote  it  by  u,  then  ai^x  is  the  component  of  this  velocity 
perpendicular  to  the  earth's  axis.  We  therefore  have  u  :  x  — 
I  :  sin  /,  or  ;r  =  u  sin  /.  Putting  this  expression  of  x  for  x  in 
the  last  expression  of  Fg  in  §  43,  we  get 


Fu  =  (200  -f-  v)  —  sin  /  m, 


in  which,  in  analogy  with  the  expression  of  Fv  in  §  46,  Fu  is 
put,  instead  of  Ff,  for  the  force  deflecting  to  the  right  or  east 
of  the  direction  of  motion  of  the  polar  component  of  velocity^. 

By  comparing  this  expression  with  that  of  Fv  in  §  46,  it  is 
seen  that  they  are  very  similar ;  in  this  a  polar  component  of 
velocity  u  gives  rise  to  a  force  deflecting  to  the  right  of  the 
direction  of  this  component,  and  in  the  other  an  east  com- 
ponent of  velocity  v  gives  rise  to  a  force  also  deflecting  to  the 
right  of  the  direction  of  this  component.  And  it  is  also  seen 
that  these  forces  are  precisely  equal  if  u  and  v  are  equal. 
When  the  directions  of  motion  are  reversed  and  u  and  v  become 
negative,  of  course  the  deflecting  forces  are  reversed  in  their 
directions  of  action,  but  the  deflecting  force  is  still  toward 
the  right  of  the  directions  of  these  components.  This  must 
be  understood  of  the  northern  hemisphere  where  sin  /  is 
positive.  In  the  southern  hemisphere,  where  sin  /  is  negative, 
of  course  the  deflecting  forces  are  reversed  in  the  directions  of 
their  actions,  and  are  always  to  the  left  of  the  directions  of  the 
components,  whether  these  are  north  or  south,  or  east  or  west. 

We  have  by  definition  in  §  45,  n  =  oo/r ;  and  if,  by  analogy, 
we  put  v  =  v/r ,  we  shall  have  v  equal  to  the  relative  gyratory- 
velocity  of  the  body  around  the  earth's  axis  in  terms  of  the 
radius,  as  n  is  the  absolute  gyratory  velocity,  in  the  same 
terms,  of  a  body  fixed  on  the  earth's  surface.  Substituting  n 


RESULTANTS  OF   THE    TWO  FORCES  AND  MOTIONS.     71 

and  v  for  their  equivalents  in  the  preceding  expressions  of  Fu 
and  F, ,  we  get 

Fu  =  (2n  -\-v)u  sin  /  m  ; 

Fv  =  (2n  -}-  v)v  sin  /  w. 

RESULTANTS   OF  THE   TWO   FORCES  AND   MOTIONS. 

50.  Where  the  motion  of  a  body  upon  the  earth's  surface 
is  such  as  to  change  both  its  longitude  and  latitude  at  the  same 
time,  both  of  the  preceding  forces  are  called  into  play  at  the 
same  time,  and  they  give  rise  to  one  resultant  force  in  a  certain 
determinate  direction.  If,  in  Fig.  7,  we  let  AB  represent  the 


Fig.  7. 

velocity  u  and  direction  of  the  polar  component  of  motion,  and 
AC,  at  right  angles  to  AB,  the  east  component  of  velocity; 
then  AD,  the  diagonal  of  the  parallelogram,  which  we  shall 
denote  by  s,  represents  the  resultant  velocity.  But  the  forces 
arising  from  the  component  velocities,  which  act  in  directions 
toward  the  right  and  at  right  angles  to  the  directions  of  mo- 
tion, and  consequently  at  right  angles  to  each  other,  may  be 


72     MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACE* 

icpresented  by  the  lines  AB'  and  AC ',  drawn  perpendicular  to, 
and  to  the  right  of,  the  directions  of  motion,  and  from  what  is 
shown  in  the  preceding  expressions  of  Fu  and  Fvy  they  are 
proportional  to  the  velocities  u  and  v  respectively.  Complet- 
ing the  parallelogram,  the  diagonal  AD'  then  represents  the 
resultant  of  the  two  forces,  both  in  magnitude  and  direction, 
and  as  the  forces  represented  by  AB'  and  AC'  have  been 
denoted  by  Fu  and  Fv  respectively,  we  may  let  Fs  denote,  by 
analogy,  the  resultant  force  represented  by  AD',  since  it 
depends  upon  the  resultant  velocity  s,  just  as  the  others  do 
upon  the  component  velocities  u  and  v.  Now  by  a  well-known 
theorem  we  have  the  diagonal  of  a  parallelogram  equal  to  the 
square  root  of  the  sum  of  the  squares  of  two  contiguous  sides. 
Hence  we  have 


s=  iV+y,     and     Fs  = 

If  we  now  square  both  members  of  the  last  two  equations 
of  §  49  and  take  the  square  roots  of  their  sums,  we  get,  by 
putting  s  and  Fs  for  their  equivalents  above, 

Fs  =  (2n  -f-  v)s  sin  /  m. 

Since,  by  the  construction  of  the  figure  and  the  relations  of 
the  homologous  sides  of  similar  triangles,  we  have  AB  :  AC 
(=  BD)  =  AB'  :  AC(=B'D'\  and  so  the  angle  BAD  equal  the 
angle  B'AD',  by  adding*  the  angle  CAD  to  both,  we  have  the 
angle  BAC  equal  the  angle  DAD' ,  and  hence  the  latter  is  a 
right  angle.  The  direction,  therefore,  of  the  resultant  of  the 
two  deflecting  components  is  at  right  angles  to  the  direction  of 
the  resultant  motions,  of  which  the  velocity  is  represented  by 
the  line  AD  or  s.  As  the  components  of  velocity?/  and  v  may 
have  any  value,  either  positive  or  negative,  the  resultant  motion 
with  velocity  s  may  have  any  direction,  and  the  resultant 
deflecting  force  will  always  be  at  right  angles  to,  and  to  the 
right  of,  this  direction  in  the  northern  hemisphere,  where  sin  / 
is  positive,  but  to  the  left  in  the  southern  hemisphere,  where 
sin  /  is  negative,  and  where,  consequently,  the  resultant  force 


RESULTANTS  OF   THE    TWO  FORCES  AND  MOTIONS.      73 

Fs  is  reversed  in  direction.  This  deflecting  force,  however,  is 
not  a  real  force,  but  is  of  the  same  nature  as  centrifugal  force, 
§  35;  and  as  it  always  acts,  as  we  have  just  seen,  in  a  direction 
at  right  angles  to  the  direction  of  motion,  its  tendency  is  to 
continually  change  direction  only,  and  not  to  increase  or 
decrease  velocity  and  momentum.  But  this  change  of  direc- 
tion must  not  be  understood  to  be  a  change  of  absolute  direc- 
tion in  space,  for  this  would  require  a  real  force,  but  simply  a 
change  of  direction  relative  to  the  earth's  surface. 

51.  In  obtaining  the  preceding  expression  of  Ft,  the  only 
condition  with  regard  to  any  real  force  to  which  the  body  may 
be  subject  was  that  it  shall  act  only  in  the  plane  of  the  meridian, 
and  so  one  component  of  the  force  be  a  central  force,  directed 
toward  the  earth's  axis.  The  initial  values  of  u  and  z>,  and  so 
of  s,  are  entirely  arbitrary,  and  the  value  of  the  latter  is  only 
changed  subsequently  by  the  action  of  the  real  force  acting 
upon  the  body,  in  a  direction  either  toward  or  from  the  pole. 
We  consequently  have  no  relation  between  the  force  and  the 
value  of  s,  and  the  value  of  the  preceding  expression  at  any 
time  depends  simply  upon  that  of  s,  and  in  no  way  upon  the 
force  acting  upon  the  body  by  which  the  value  of  s  is  changed. 
The  preceding  expression  of  Fs,  therefore,  holds  when  the  force 
is  infinitely  small,  and  so  when  it  entirely  vanishes  and  the 
value  of  s  and  the  direction  of  motion  depend  upon  an  in- 
stantaneous impulse.  This  expression,  therefore,  holds  wher- 
ever the  body  has  a  motion  in  any  direction  relative  to  the 
earth's  surface,  in  whatever  way  this  motion  may  have  been 
produced.  If  a  body,  therefore,  were  set  in  motion  upon  the 
spheroidal  surface  of  the  earth,  supposed  to  be  perfectly  smooth 
and  without  friction,  it  would  continue  to  move  on  forever  with 
its  initial  velocity,  but  with  continually  changing  direction 
relative  to  the  earth's  surface,  and  its  path  would  vary  very 
much  with  different  initial  velocities.  It  is  seen  from  the 
expression  of  Fs  that  the  deflecting  force,  for  the  same  value 
of  s,  would  differ  with  different  directions  of  motion,  since 
v  =  v/r  is  a  function  of  v,  which  is  the  east  component  of  s, 
and  so  changes  with  different  directions,  and  even  becomes 


74    MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACE* 

negative  when  v  becomes  a  west  component,  as  it  may  in 
many  cases  even  where  the  initial  direction  is  east.  It  is  also 
seen  that  this  force  varies  with  latitude,  so  that  if  the  initial; 
velocity  given  were  great,  the  body  might  be  carried  from  a 
high  latitude  down  to  a  very  low  one,  when  sin  /  and  conse- 
quently the  whole  expression  would  be  small,  or  it  might 
even  be  carried  across  the  equator  into  the  opposite  hemi- 
sphere, where  the  deflecting  force  would  be  changed  from  the 
right-hand  to  the  left-hand  side  of  the  direction,  or  the  contrary, 
according  to  the  hemisphere  from  which  it  passes. 

In  case  the  earth  had  no  rotation  around  its  axis,  n  in  the 
preceding  expression  of  Ft  would  vanish,  and  it  would  then  be 
the  expression  of  the  deflecting  force  due  simply  to  the  cen- 
trifugal force  of  the  motion  of  the  body.  But  it  must  be  here 
borne  in  mind  that  these  so-called  forces,  as  they  have  beerr 
defined  and  used,  are  not  real  forces,  but  simply  tendencies  to 
cause  departures  from  the  parallels  and  meridians.  If  the 
initial  motion  is  in  the  direction  of  the  meridian,  then  v,  and 
consequently  v  =  v/r,  vanishes,  and  so  the  expression  of  F3  van- 
ishes, and  consequently  there  is  no  tendency  of  the  body  to 
depart  to  either  side  of  the  meridian.  But  if  the  initial  motion* 
is  in  the  direction  of  a  parallel  of  latitude,  then  we  have  s  —  v, 
and  the  expression  then  simply  becomes  that  of  the  horizontal" 
component  of  the  centrifugal  force  of  the  body  in  its  motion  along 
the  parallel,  and  Fs  is  then  the  force  with  which  the  body  tends- 
to  depart  from  this  parallel,  and  of  the  lateral  pressure  of  the 
body  in  a  direction  from  the  pole  toward  the  equator  if  the 
body  were  constrained  to  move  in  a  groove  on  a  given  parallel. 
Since  in  this  case  s  becomes  the  same  as  v,  the  expression  has 
the  same  sign  and  the  force  the  same  direction  of  action,, 
whether  the  initial  motion  is  east  or  west.  At  the  equator, 
where  sin  /=o,  this  force  vanishes,  as  in  the  case  where  the 
initial  motion  is  in  the  direction  of  the  meridian,  and  the  body- 
moves  in  the  great  circle  of  the  equator. 


WHERE    THE   CENTRE   OF  FORCE  IS  NOT   THE  POLE.     75; 


WHERE  THE  CENTRE   OF  FORCE   IS   NOT  THE  POLE. 

52.  In  what  precedes,  it  has  been  supposed  that  the  body  is 
not  acted  upon  by  any  real  force  tending  to  move  it  out  of  the 
plane  of  the  meridian.  We  come  now  to  consider  the  case  in 
which  there  is  some  force  tending  to  drive  the  body  either 
toward  or  from  some  point  on  the  earth's  surface  which  is  not 
one  of  the  poles,  and  for  the  sake  of  simplicity  we  shall  here 
limit  the  case  to  a  portion  of  the  earth's  surface  around  this 
centre  which  is  not  so  great  that  it  cannot  be  regarded,  without 
material  error,  as  a  plane  surface.  Let  us,  by  way  of  introduc- 
tion to  what  is  to  follow,  consider  first  the  case  of  a  limited 
area  around  the  north  pole.  In  this  case  if  the  area  does  not 
extend,  say,  more  than  ten  degrees  from  the  pole,  then  we  can 
regard  sin  /  for  this  whole  area  as  being  equal  to  unity,  without 
any  material  error  arising  from  such  an  assumption  ;  and  then 
we  get  from  the  expressions  of  FH  and  Fv ,  §  49,  by  putting 
sin  /  =  i , 

Fu  =  (211  -\-  v)u  .  m ; 
Fv  =  (2n  -f-  v)v  .  m. 

We  have  here  the  case  of  the  gyrating  concave  disk  of 
§  39,  the  concavity  being  that  arising  from  the  spheroidicity  of 
the  earth's  surface,  and  being  such  that  the  tendency  of  a  body 
at  rest  to  slide  down  toward  the  pole  is  exactly  counteracted  by 
the  centrifugal  force  due  to  the  earth's  rotation. 

The  value  of  n  in  this  case  is  that  of  the  earth's  rotation  on 
its  axis.  If  the  centre  of  the  area  considered  were  on  the 
equator,  there  would  be  no  gyratory  motion  of  this  area  around 
the  centre,  though  of  course  the  centre  and  the  whole  area 
would  gyrate  around  the  earth's  axis,  but  not  around  any  axis 
in  the  plane  of  the  equator.  In  this  case,  therefore,  we  have 
n  =  o.  It  is  reasonable  to  suppose,  therefore,  that  the  value  of 
n  is  the  greatest  at  the  pole,  and  decreases  with  decrease  of 
latitude,  according  to  some  function  of  the  latitude,  from  the- 


76    MOTIONS  OF  BODIES  RELATIVE    TO   EARTH'S  SURFACE. 

pole  to  the  equator.  This  function,  it  is  well  known,  is  the 
sine  of  the  latitude.  Assuming  this  here  without  attempting  to 
demonstrate  it,  if  we  put  ri  for  the  gyratory  velocity  in  terms 
of  the  radius  around  any  point  on  the  parallel  of  latitude  /,  we 
shall  have 

ri  =  n  sin  /. 

Putting  n'  or  n  sin  /  instead  of  n  in  the  preceding  expres- 
sions, they  become 

FH  =  (2n  sin  /-)-  r)u  .  m, 
Fv  =  (2n  sin  l-\-  v)v  .  m, 


in  which  u  is  the  velocity  toward  the  centre  and  v  is  the  gyra- 
tory velocity  around  that  centre,  and  v  =  v/rt  in  which  r  is  the 
distance  from  the  centre.  The  first  of  these  is  the  expression 
of  the  gyratory  force,  and  corresponds  to  the  last  expression  of 
Fs  in  §  43  ;  and  the  second  is  the  expression  of  force  from  the 
•centre,  and  corresponds  to  the  last  expression  of  Fe  in  §  40,  since 
n  sin  /  =  n'  is  the  angular  gyratory  velocity  around  the  centre 
:in  this  case. 

The  resultant  of  these,  taken  as  in  §  50,  is 

Fs  =  (2n  sin  l-\-v)s  .  m. 

As  in  the  preceding  case,  this  expression  varies  with  different 
•directions  of  motion  of  velocity  s,  since  v  =  v/r  varies  as  v 
varies,  and  this  being  one  of  the  components  of  s  changes  with 
change  of  direction  for  the  same  value  .of  s,  and  may  even  be- 
come negative  —  as  in  the  case  in  which  the  relative  gyratory 
velocity  is  in  a  direction  contrary  to  that  of  the  area  under  con- 
sideration, depending  upon  the  earth's  rotation. 

As  is  usual  in  the  case  of  a  central  force,  the  value  of 
r  =  v/r  may  become  very  great  in  comparison  with  2.n  or 
2n  sin  /;  for  not  only  does  the  value  of  v  become  very  great 
near  the  centre,  but  r  becomes  very  small,  and  so  for  both 
reasons  v  becomes  large  near  the  centre.  In  such  cases  the 
motion  of  the  body  becomes  mostly  a  rapid  gyration  around 
the  centre,  and  the  deflecting  force  is  almost  entirely  the  cen- 


THE  DEFLECTING  FORCE   OF    THE   EARTH'S  ROTATION.      77 

trifugal  force  arising  from  the  relative  gyratory  velocity  of  the 
body,  the  part  depending  upon  n  in  such  cases  being  very  small 
in  comparison  with  that  depending  upon  v  —  v/r. 


THE   DEFLECTING  FORCE   OF   THE   EARTH'S    ROTATION. 

53.  We  have  seen  from  what  precedes  that  wherever  a  body 
upon  the  earth's  surface  has  a  motion  relative  to  that  surface, 
however  produced,  there  is  a  deflecting  force,  depending  in 
part  upon  the  earth's  rotation,  and  partly  upon  the  velocity 
and  direction  of  motion  relative  to  the  earth's  surface,  and  en- 
tirely independent  of  any  real  forces,  by  which  the  body  is  con- 
tinually acted  upon  in  a  direction  at  right  angles  to  the  direc- 
tion of  motion  and  deflected  from  its  course,  and  that  this,  in- 
the  case  of  central  forces,  may  become  very  great  near  the  cen- 
tre of  force,  where  the  value  of  r,  the  distance  from  the  centre, 
is  small.  In  all  straight-lined  motions  on  the  earth's  surface,, 
the  value  of  r  in  the  expression  of  v  —  v/r  becomes  infinite,  and 
so  the  value  of  v  in  the  preceding  expression  of  Fs  vanishes,, 
and  the  whole  deflecting  force  depends  upon  the  earth's  rota- 
tion. In  the  case  also  in  which  the  body  is  not  acted  upon  by  a 
local  force  but  is  subject  only  to  a  force  acting  in  the  plane  of  the 
meridian,  the  value  of  v  in  the  expression  of  Fs,  §  50,  is  very  small 
in  comparison  with  2n,  unless  it  should  be  very  near  the  pole, 
where  r,  in  the  expression  of  v  =  v/r,  is  the  distance  from  the 
earth's  axis.  It  is  seen  from  Table  V  that  the  value  of  2oo  on  the 
parallel  of  45°  is  658  meters  per  second  ;  so  for  a  relative  easterly 
velocity  v  of  any  body  of  only  20  meters  per  second  (45  miles 
per  hour),  the  ratio  of  v  to  2u  sin  /  in  the  expression  of  Ft  is  as 
20  to  658,  since  v  =  v/r  and  2n  sin  /=  2(&/r.  For  any  ordinary 
velocity,  therefore,  on  the  earth's  surface  where  the  body  is 
not  subject  to  the  action  of  a  strong  local  central  force,  the 
whole  deflecting  force  depends  mostly  upon  the  influence  of 
the  earth's  rotation,  and  is  almost  entirely  independent  of  the 
centrifugal  force  arising  from  the  relative  motion  on  the 
earth's  surface,  which  would  exist  in  case  the  earth  had  no> 
rotation  on  its  axis. 


78     MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACE. 

For  the  part  of  the  deflecting  force  depending  only  upon  the 
-earth's  rotation,  we  obtain  either  from  the  expression  of  Fs  in 
§  50,  or  the  last  one  in  §  52,  by  neglecting  the  part  independent 
of  n, 

Fs  =  2ns  sin  / m. 

In  the  northern  hemisphere  this  force  acts  in  a  direction  at 
Tight  angles  to  the  direction  of  motion,  and  to  the  right;  but 
in  the  southern  hemisphere,  where  sin  /  is  negative,  the  direc- 
tion is  reversed,  and  consequently  at  right  angles  to  the  left. 
It  is  seen  from  the  preceding  expression  that  this  force,  for  any 
given  mass,  depends  simply  upon  the  sine  of  the  latitude  and 
the  velocity  s  of  the  relative  motion  and  is  entirely  independ- 
ent of  the  direction  of  this  motion.  Hence,  if  a  body  moves  in 
•  any  direction  upon  the  earth's  surface,  there  is  a  deflecting  force 
arising  from  the  earths  rotation,  which  deflects  it  to  the  right  in  the 
northern  hemisphere,  but  to  the  left  in  the  southern  hemisphere* 

54.  This  important  part  of  the  subject  may  be  viewed  in  a 
different  manner,  and  one  by  which  it  may  perhaps  be  more 
readily  understood  by  many  readers,  than  by  the  preceding 
method  of  considering  the  matter.  If  a  body  at  a,  Fig.  8,  has 


m 

Fig.  8. 

a  motion  with  uniform  velocity  in  the  direction  from  m  to  n,  or 
the  contrary,  in  the  line  mn,  which  is  continually  and  uniformly 
changing  its  direction  from  right  to  left  of  the  direction  of  mo- 
tion, it  is  readily  seen  that  as  the  line  changes  its  direction,  the 
body  by  virtue  of  its  inertia  has  a  tendency  to  continue  on  in 
the  same  direction,  and  to  depart  from  the  gyrating  line  to  the 

*  This  important  proposition  was  first  demonstrated  by  the  present  writer  in 
the  year  1859  in  a  paper  on  "The  Motions  of  Fluids  and  Solids  on  the  Earth's 
Surface,"  published  in  Runkle's  Mathematical  Monthly.  This  part  of  that  paper 
appeared  in  the  May  number  of  the  Monthly.  The  whole  paper  has  since  been 
•republished  by  the  Signal  Service  (Professional  Paper  No.  VIII),  with  extensive 
notes  by  Professor  Frank  Waldo. 


-THE  DEFLECTING  FORCE    OF    THE  EARTH'S  ROTATION.      79 

right,  just  as  it  would  from  a  line  fixed  in  space  if  there  was  a 
constant  real  force  acting  on  the  body,  at  right  angles  to  the 
direction  of  motion.  If  the  body  moved  in  the  contrary  way 
from  n  towards  ;;/,  the  tendency  would  be  to  depart  on  the 
other  side,  but  still  to  the  right  of  the  direction  of  motion, 
where  the  line  gyrates  from  right  to  left,  looking  in  the  direc- 
tion of  motion.  It  is  also  evident  that  if  the  line  is  changing 
its  direction  from  left  to  right,  the  body  tends  to  depart  from 
this  line  to  the  left-hand  side.  But  if  the  body  were  not  free 
to  move  in  a  fixed  direction  in  space,  but  were  compelled  to 
move  in  the  line  continually  and  uniformly  changing  its  direc- 
tion, as  in  a  groove,  then,  instead  of  departing  to  the  right-  or  the 
left-hand  side,  as  the  case  may  be,  it  would  press  against  the 
.side  with  a  force  sensibly  equal  to  a  real  force  which,  during 
a  very  small  interval  of  time,  would  cause  the  body  to  depart 
from  a  fixed  line  in  space  at  the  same  rate.  It  is  readily  seen 
that  this  rate  of  departure  at  any  instant  of  time  must  be  pro- 
portional to  the  velocity  s  in  the  direction  of  motion,  and  the 
rate  of  change  of  direction,  or  the  gyratory  velocity  of  the  line 
in  terms  of  the  radius.  Denoting  this  latter  by  n't  it  is,  there- 
fore, proportional  to  n' s,  and  consequently  the  lateral  pressure, 
where  the  body  is  constrained  to  move  in  a  straight  line  with 
changing  direction  in  space,  is  in  the  same  proportion. 

Some  general  idea  of  this  deflecting  force  may  be  formed 
from  the  experience  of  any  one  in  walking  over  a  narrow  draw- 
bridge while  it  is  turning  around  its  central  pivot.  If  there  were 
no  railings,  the  tendency  would  be,  if  not  guarded  against,  to 
run  off  on  the  one  side  or  the  other,  according  to  the  direction 
of  gyration  ;  and  where  there  are  railings,  to  press  against  that 
side.  And  this  tendency  would  evidently  be  in  proportion  to 
the  velocity  of  transit  across  the  bridge  and  the  angular  veloc- 
ity of  its  gyration.  Of  precisely  the  same  nature  is  the  deflect- 
ing force  of  the  earth's  rotation;  for  every  horizontal  line,  fixed 
relatively  to  the  earth's  surface,  except  at  the  equator,  is  con- 
tinually changing  its  direction  with  reference  to  a  direction 
fixed  in  space;  and  so  a  body,  set  in  motion  in  any  direction 
relative  to  the  earth's  surface,  tends,  if  free,  to  depart  from 


80    MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACED 

this  direction,  and  if  constrained  to  move  as  in  a  groove  in  this 
direction,  to  press  toward  one  side  or  the  other,  as  the  case 
may  be. 

55.  The  absolute  amount  of  deflecting  force  may  be  de- 
duced in  the  following  manner :  If  a  body  at  a,  Fig.  8,  has,  at 
any  instant  of  time,  a  motion  in  the  direction  from  m  toward  n 
in  the  line  mn  with  the  velocity  s,  and  this  line  at  the  same 
time  is  changing  its  direction  or  gyrating  around  the  point  a, 
whatever  other  motion  the  whole  line  may  have,  with  a  gyra- 
tory velocity  n1  in  terms  of  the  radius,  then  if  ab  represents  s,. 
and  the  angle  nan'  the  change  of  direction  in  a  unit  of  time, 
this  unit,  which  is  entirely  arbitrary,  being  taken  so  small  that 
this  angle  is  very  small  and  ab  is  sensibly  equal  to  ac,  be  being 
perpendicular  to  m'n'  and  measuring  the  nearest  distance  of 
the  point  b  from  m'n',  the  body  at  the  end  of  this  unit  of  time 
is  departing  from  the  line  m'n'  by  the  space  be  in  a  unit  of  time 
by  virtue  of  its  velocity  s  in  the  direction  of  mn.  But  this 
perpendicular  at  the  distance  of  unity  from  a  is  n',  and  there- 
fore the  body  in  moving  through  the  space  s  in  a  unit  of  time 
departs  from  the  line  m'n' ,  supposed  to  remain  fixed  for  the 
time,  by  the  space  n's.  If  we  now  suppose  that  when  the  body 
arrives  at  b  it  remains  stationary  for  the  time,  then  the  line 
m'n',  by  virtue  of  its  change  of  direction,  or  gyratory  velocity 
n'  around  the  point  a  at  the  distance  of  unity,  is  departing  from 
the  body  at  b,  which  is  at  the  distance  s  from  a,  at  the  rate  of 
ns.  Therefore  by  virtue  of  both  the  motions  of  the  body  in  its 
direction  mn,  fixed  in  space,  and  also  of  the  uniform  change  of 
direction  of  the  line  m'n',  the  body  at  the  end  of  the  unit  of 
time  is  departing  from  the  line  of  varying  direction  in  space  at 
the  rate  of  2n's  in  a  unit  of  time.  It  is  therefore  departing 
from  it  at  the  same  rate  that  a  body  moving  in  a  direction  fixed 
in  space  would  be  drawn  out  of  the  line  of  this  direction  by  a 
force  acting  in  a  direction  at  right  angles  to  the  direction  of 
motion,  if  the  acceleration  of  this  force  were  2n's.  The  lateral 
pressure,  therefore,  of  a  body  of  the  mass  m,  if  constrained  to 
move  in  the  line  of  varying  direction,  is  2n's  .  m.  In  case  of  a 
straight  line  on  the  earth's  surface,  at  any  given  parallel  /,  we 


THE  DEFLECTING  FORCE    OF   THE  EARTH'S  ROTATION.      8  1 

have  seen  that  the  value  of  ri  is  n  sin  /.  Denoting,  therefore, 
as  before,  this  deflecting  force  of  a  body,  of  velocity  j,  by  Fs  , 
and  putting  n  sin  /  for  n'  ',  we  have,  as  in  §  53, 

Ft  =  2ns  sin/,  m. 

In  the  southern  hemisphere  the  line  m'n'  would  gyrate,  with 
reference  to  the  line  mn  fixed  in  space,  from  left  to  right  ;  and 
so  in  this  hemisphere  the  deflecting  force,  or  tendency  to  de- 
part from  the  line  m'n'  ,  is  to  the  left-hand  side. 

56.  If  the  body  in  motion  were  a  stratum  of  liquid,  as  the 
water  of  a  wide  river,  moving  with  a  velocity  s  in  any  uniform 
direction,  then  the  deflecting  force  at  right  angles  to  this  direc- 
tion would  cause  an  ascending  gradient  of  the  surface  and  of 
all  strata  of  equal  pressure  in  that  direction,  and  this,  as  ex- 
plained in  the  case  of  the  gradient  arising  from  centrifugal 
force,  §  38,  would  be 

Fs         2ns  sin  / 

sn 


putting  for  n  and  g  their  numerical  values  in  §  45  in  obtaining 
the  last  form  of  this  expression. 

The  value  of  e  being  the  change  of  level  in  the  distance  of 
unity,  which  in  this  expression  is  the  meter,  for  a  distance  of  r 
meters  the  change  of  level  is  re.  If  a  river  one  mile  in  width 
(1609  m.)  has  a  velocity  of  2  meters  per  second  (4.5  miles  per 
hour)  in  any  uniform  direction  on  the  parallel  of  45°,  then  the 
surface  of  the  right-hand  side  in  the  northern  hemisphere  stands 
higher  than  the  other  by 

re  —  0.00001487  X  1609  X  2  X  0.707  =  0.034^  =1.3  inches, 

in  which  0.707  is  sin  45°,  taken  from  Table  V  or  any  table  of 
natural  sines. 

The  values  of  e/s  have  been  computed  from  the  formula 
above,  for  each  fifth  parallel  of  latitude,  and  given  in  Table  V, 
from  which  the  values  of  re  can  be  more  conveniently  obtained. 
Thus  from  the  table  we  get  for  the  parallel  of  45°,  e/s  equal  to- 


82     MOTIONS   OF  BODIES  RELATIVE    TO  EARTH'S  SURFACE. 

0.00001052  ;  and  so  in  the  example  above,  we  have,  as  just  ob- 
tained, 

re  =  2  X  1609  X  0.00001052  =  o.034m. 

The  value  of  e  above,  since  it  is  the  ratio  between  the  de- 
flecting force  and  that  of  gravity,  expresses  also  the  ratio  be- 
tween the  lateral  pressure,  due  to  the  earth's  rotation,  of  a  body 
moving  in  any  uniform  direction  with  velocity  s,  and  the  verti- 
cal pressure  of  the  body.  Multiplying,  therefore,  the  value  of 
e/s  in  the  table  by  s,  we  get  this  ratio.  Hence  if  a  railroad  car 
on  the  parallel  of  40°  moves  with  a  velocity  of  20  meters  per 
second  (45  miles  per  hour),  we  get 

e  =  0.00000956  X  20  =  0.0001912. 

The  lateral  pressure  is  therefore  about  1/5230  part  of  the  ver- 
tical pressure  of  the  car.  If  the  road  had  a  curvature  of  radius 
r,  then  the  pressure  arising  from  the  centrifugal  force,  as  given 
in  §  37,  would  have  to  be  added,  in  the  northern  hemisphere, 
if  the  motion  of  the  car  was  from  right  to  left  around  the  cen- 
tre of  curvature,  but  subtracted  if  the  contrary  way,  in  order  to 
obtain  the  pressure  to  the  right  of  the  direction  of  motion. 
It  is  to  be  understood  of  course  that  the  two  rails  of  the  road 
are  on  the  same  level. 

For  intermediate  latitudes  of  the  five-degree  intervals  of 
the  table  the  value  of  e/s  is  readily  obtained  by  interpolation 
with  sufficient  accuracy  by  using  only  the  first  differences.  Thus, 
if  the  value  of  e  is  required,  for  the  latitude  of  52°,  correspond- 
ing to  a  wind  velocity  of  1 5  meters  per  second,  we  readily  ob- 
tain from  the  table,  by  adding  2/5  of  80  to  0.00001139,  e/s  = 
0.00001171.  Hence  we  have 

e  —0.00001171  X  15  =  0.0001756. 

57.  The  value  of  e,  for  any  given  velocity  s,  is  the  difference 
-of  level  of  the  surface  of  any  inelastic  fluid,  or  of  a  stratum  of 
equal  pressure  in  the  case  of  the  atmosphere,  between  two 


THE  DEFLECTING  FORCE   OF   THE  EARTH'S  ROTATION.      83 

stations  at  the  distance  of  unity.  Or,  e  is  the  height  of  the 
column  of  the  fluid,  subject  to  the  force  of  gravity,  which  ex- 
actly counterpoises  a  horizontal  column  of  a  unit  in  length  and 
of  the  same  base,  subject  to  the  action  of  the  deflecting  force 
causing  the  gradient.  The  height  of  this  column  is  a  measure 
of  the  difference  of  pressure  on  a  horizontal  surface  at  the  dis- 
tance of  unity,  and  the  vertical  pressure  of  such  a  column  of 
unit  base  would  express  the  difference  of  pressure  on  such  a 
base  in  kilograms  or  pounds  of  pressure  according  to  the  meas- 
ure adopted.  In  the  case  of  the  atmosphere,  however,  the 
gradient  is  usually  measured  by  the  height  of  the  mercurial  col- 
umn which  exactly  counterpoises  the  lateral  pressure  on  the 
same  base,  §  10,  and  this  is  called  the  barometric  gradient.  But 
in  expressing  this  gradient  we  do  not  use  the  meter  as  the 
unit  of  length,  but  use  the  millimeter  in  the  vertical  height 
of  the  mercury  and  one  degree  of  a  great  circle,  or  1 1 1,1 11  me- 
ters, as  the  unit  of  horizontal  distance.  The  height,  also,  of 
the  mercurial  column  is  less  than  that  of  the  air  column  of 
standard  pressure  and  temperature,  in  the  ratio  of  the  density 
of  such  an  air  column  to  that  of  mercury,  or  as  I  to  10,517. 
In  order,  therefore,  to  obtain  the  barometric  gradient,  which 
we  shall  denote  by  G,  from  the  preceding  general  expression 
of  e,  it  is  necessary  to  multiply  this  expression  by  1000,  on  ac- 
count of  a  change  of  the  unit  of  the  vertical  column  from  the 
meter  to  the  millimeter,  and  also  by  111,111  on  account  of  the 
change  of  the  unit  of  horizontal  distance,  and  to  divide  by  10,517 
on  account  of  the  height  of  the  mercurial  column  being  less 
than  that  of  the  counterpoising  air  column  in  the  ratio  of  I  to 
10,517.  We  then  get 

Gl  =  O.I57U  sin  /. 

But  it  must  be  understood  that  this  is  only  for  air  of  standard 
pressure  and  temperature.  For  any  other  it  must  be  increased 
or  diminished  directly  as  the  pressure  of  the  air  and  inversely  as 
the  absolute  temperature,  since  the  density  of  the  air  by  the  laws 
of  Boyle  and  of  Charles,  §  4,  changes  in  these  ratios.  Putting, 
.therefore,  as  heretofore,  P0  for  the  standard  pressure  P,  and  T^ 


84    MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S   SURFACE.. 

for  the  standard  absolute  temperature    T,  we  obtain  the  fol- 
lowing more  general  expression  : 


P    T 
sin  l-'- 


But  this  expression  holds  only  in  the  case  of  straight-lined 
winds  with  little  or  no  friction,  where  the  direction  of  gradient 
is  at  right  angles  to  that  of  the  wind. 

The  preceding  less  general  expression  of  G^  gives  values  at 
the  earth's  surface  and  for  all  ordinary  temperatures,  which  are 
sufficiently  accurate  for  most  purposes,  and  these  are  given  in 
Table  V  for  unit  of  velocity.  For  other  velocities  it  is  only 
necessary  to  multiply  the  tabular  numbers  into  the  velocity.. 
Thus  on  the  parallel  of  40°,  for  a  wind  of  15  meters  per  second, 
we  get  in  millimeters 

G  =  o.ioio  X  15  =  1.51. 

By  reversing  the  preceding  expressions,  the  value  of  s,  the 
velocity  of  the  wind,  may  be  found  corresponding  to  any  given 
gradient.  By  the  preceding  example,  if  there  is  an  observed 
gradient  of  1.5  mm.,  the  corresponding  wind  velocity  in  a  direc- 
tion at  right  angles  to  that  of  the  gradient  must  be  about  15 
meters  per  second. 

All  the  preceding  gradients  depend  upon  n,  and  so  upon  the 
earth's  rotation,  and  would  vanish  if  the  earth  were  at  rest.  In 
addition  to  these  there  may  be  gradients  depending  upon  the 
centrifugal  force  when  the  wind  blows  in  circuits,  and  these 
may  be  very  great  if  the  radius  of  curvature  is  small  and  the 
velocity  large. 

In  order  to  obtain  the  gradient  G  in  the  case  of  centrifugal 
force  in  connection  with  that  of  the  earth's  rotation,  we  must 
use  the  expression  of  Fs  ,  §  52,  instead  of  the  preceding  one  of 
Ft.  We  thus  get,  by  multiplying  by  1000,  by  1  1  1,1  1  1,  and  divid- 
ing by  10,517, 

272  sin  /+  v          ill  ill  in 
G'= 


9.806  10517 


THE  DEFLECTING  FORCE   OF   THE  EARTH'S  ROTATION.     8$ 

By  neglecting  v,  the  part  depending  upon  the  centrifugal  force, 
and  giving  n  its  value  0.00007292,  we  get  the  first  of  the  two  pre- 
ceding expressions  of  G,  in  the  case  of  standard  temperature 
and  pressure.  The  general  expression  of  this,  for  any  pressure 
P  and  absolute  temperature  T,  becomes 


P    T 
(zn  sin7+*)^r-  ~. 


in  which  v  =  v/r. 

The  relation  of  the  part  of  the  gradient,  whether  the  linear 
gradient  e  or  the  barometric  gradient  G,  depending  upon  the 
curvature  of  the  path,  to  that  depending  upon  the  earth's  rota- 
tion is  given  by  the  relation  between  v  =  v/r  and  2n  sin  / 
in  the  expressions  of  the  deflecting  forces  in  §  52.  Thus, 
if  a  body  on  the  parallel  of  45°  moves  with  a  velocity  of  20 
meters  per  second,  and  has  a  radius  of  curvature  of  400 
kilometers  (400000  meters,  or  250  miles  nearly)  we  have 
w/r  =  20/400000  =  0.00005,  while  the  value  of  2n  sin  /,  from 
Table  V,  is  0.000103  ;  and  therefore  the  tabular  gradient  must 
be  increased  in  the  ratio  of  the  sum  of  these  quantities  to  the 
latter,  or  nearly  one  half,  for  the  effect  of  curvature  and  its 
consequent  centrifugal  force. 

58.  If  a  body  has  a  motion  of  uniform  velocity  in  any  direc- 
tion, however  produced,  over  the  earth's  surface,  supposed  to 
be  entirely  smooth  and  without  friction,  and  the  velocity  is  such 
that  the  range  of  motion  in  latitude  is  so  small  that  sin  /  can 
be  regarded  as  a  constant,  then  the  lateral  deflecting  force  is 
constant,  and  the  body  is  being  continually  deflected  from  its 
course  by  equal  angles  in  equal  times,  and  so  it  describes  a 
circle.  The  radius  r  of  this  circle  must  be  such  that  the  cen- 
trifugal force  corresponding  to  the  velocity  s,  or  (s*/r)m,  §  36,  in 
a  direction  from  the  centre  must  be  exactly  equal  to  the  de- 
flecting force  in  the  contrary  direction.  Hence,  comparing  this 
-with  the  expression  of  F,,  §  55,  we  have  s*/r  =  2ns  sin  /, 
or  • 


86    MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACE, 


r  = 


2n  sin 


Since  sin  /  =  o  at  the  equator,  r  would  be  infinite  there,  and 
consequently  the  body  would  move  sensibly  in  a  straight  line 
so  long  as  it  remained  near  the  equator.  But  if,  on  the  parallel 
of  45°,  where  sin  /  =  0.707,  the  body  should  receive  a  velocity  s 
in  any  direction  of  5  meters  per  second,  we  should  then  have 

r  =  6857  X  — j~z  =  48500  m.  =  30  miles  nearly. 


This  would  give  a  range  of  less  than  one  degree  in  latitude, 
and  consequently  sin  /  would  remain  nearly  constant. 

59.  The  acceleration  of  the  deflecting  force  Fs  ,  §  55,  is 
2ns  sin  /.  In  the  case  of  a  falling  body  the  space  passed  over 
is  given  by  the  well-known  expression  %gf,  in  which  g  is  the 
acceleration  of  gravity,  and  t  is  the  time.  So  in  the  case  of  this 
deflecting  force,  putting  2ns  sin  /  for  g,  and  d  for  the  departure 
of  the  body  from  the  tangent  or  initial  direction,  we  get  for  a 
very  short  range 

d  •=.  0.00007292^  sin  / .  f. 

If  a  rifle-ball  on  the  parallel  of  50°  is  discharged  at  a  target 
at  the  distance  of  one  kilometer  with  a  velocity  of  500  meters 
per  second,  we  have  in  this  case  t  =  2  seconds,  and  hence  we 
get  for  the  departure  d  of  the  ball  from  the  direction  of  initial 
discharge  relative  to  the  earth's  surface 

^  =  0.00007292  X  500  X  0.766  X22  =  o.i  I  meter. 

The  ball,  therefore,  in  the  northern  hemisphere,  would  deviate 
to  the  right  of  the  target  about  four  inches.  It  would  continue 
on  in  the  same  direction  in  space,  but  by  the  time  of  its  arrival 
at  the  distance  of  the  target  this  would  have  moved  around 
from  right  to  left  about  four  inches.  This  lateral  deviation, 


THE  DEFLECTING  FORCE    OF   THE  EARTH' S  ROTATION.     87 

however,  would  be  very  small  in  comparison  with  the  vertical 
deviation  downward,  due  to  gravity.  The  ratio  between  the 
two  is  that  of  the  corresponding  forces,  or  of  2ns  sin  /  to  g. 
This,  in  the  preceding  example,  is 

2  X  0.00007292  X  500  X  0.766/9.806  =  0.0057, 

and  hence  the  lateral  deviation  is  only  about  i/i  80  of  the  vertical 
one.  If,  however,  the  velocity  s  is  increased,  this  ratio  is  in- 
creased in  the  same  proportion. 

The  preceding  general  expression  of  d  is  applicable  where 
the  velocity  of  the  projectile  is  variable,  provided  s  represents 
its  mean  velocity,  just  as  in  the  case  of  a  falling  body  the  ex- 
pression \g?  would  be  applicable  if  g  were  variable,  provided 
we  should  use  the  mean  of  g  for  all  the  increments  of  time. 
Letting,  therefore,  D  represent  the  distance  to  which  the  pro- 
jectile is  cast,  we  can  put  D  —  st,  and  then  the  expression  of  d 
becomes 

d  =  0.00007292  sin  IDt. 

This  is  applicable  to  a  projectile  thrown  high  up  in  the  air,  and 
describing  approximately  a  parabolic  curve,  in  which  the  hori- 
zontal velocity  varies.  It  is  only  necessary  to  know  the  time 
and  distance.  If  a  cannon-ball  were  projected  to  the  distance 
of  5  kilometers  in  10  seconds  on  the  parallel  of  40°,  we  should 
have  for  the  lateral  deviation 

d—  0.00007292  X  0.643  X  5000  X  10=  2.35  meters. 

It  is  seen  that  the  deviations  due  to  the  earth's  rotation  are 
of  little  importance  in  gunnery ;  but  still  it  is  interesting  and 
important  to  know  of  about  what  order  these  effects  are  in 
ordinary  cases. 

60.  In  the  case  of  a  projectile  thrown  vertically  upward,  the 
condition  of  rw  =  c,  §  41,  must  be  satisfied,  so  that  the  higher 
the  projectile  and  the  greater  the  value  of  r  is,  the  less  must  be 
the  gyratory  velocity  w.  The  initial  value  of  this  at  the  earth's 
surface  for  the  different  latitudes  is  that  of  GO  in  Table  V,  and 


88     MOTIONS  OF  BODIES  RELATIVE    TO  EARTH'S  SURFACE. 

the  initial  value  of  r  =  r'  cos  /  is  the  initial  distance  of  the  body 
from  the  earth's  axis.  The  approximate  value  of  r'  is  6370 
kilometers.  Hence  we  shall  have  rw  =  637002  cos  /,  in  which 
r  is  the  distance  of  the  projectile  from  the  earth's  axis.  If  h  is 
the  height  of  the  projectile  above  the  earth's  surface,  we  have 
r  —  (6370+  Ji]  cos  /.  Hence  with  this  we  get  from  the  preced- 
ing equation 

63/0 


in  which  h  is  expressed  in  kilometers,  but  w  and  GO  may  have 
any  unit  of  measure. 

At  the  equator,  where  GO  =  465  m.,  we  have  at  the  height  of 
10  kilometers 

6370 
W  =  6380  X  4  5  =  4  4'27  m* 

Hence  the  absolute  gyratory  or  east  velocity  per  second  at 
the  altitude  of  10  kilometers  would  be  0.73  m.  less  than  that 
of  the  earth's  surface,  and  hence  there  would  be  a  west  velocity 
relative  to  the  earth's  surface  of  0.73  meters  per  second,  while 
at  lower  altitudes  the  rate  of  gain  of  the  absolute  easterly 
motion  of  the  earth's  surface  upon  that  of  the  projectile  would 
be  proportionally  less.  The  projectile,  therefore,  after  falling 
back  to  the  earth's  surface,  strikes  it  at  a  point  west  of  the 
point  from  which  it  was  projected,  since  while  at  higher  alti- 
tudes its  absolute  easterly  velocity  was  less  than  that  of  the 
point  of  the  earth's  surface  from  which  it  started.  The  dis- 
tance between  the  two  points,  of  course,  depends  upon  the 
height  to  which  the  projectile  ascends,  and  the  time  between 
leaving  and  returning  to  the  earth's  surface. 

For  other  latitudes,  it  is  seen  from  the  preceding  expression, 
iv  is  less  in  proportion  to  the  values  of  G?  in  Table  V,  or  in  the 
ratio  of  the  cosines  of  the  latitudes. 


CHAPTER  III. 
THE  GENERAL  CIRCULATION   OF  THE  ATMOSPHERE. 

INTRODUCTION. 

61.  THE  motions  of  the  atmosphere  depend,  either  directly 
or  indirectly,  upon  differences  of  temperature.  Without  these 
the  aqueous  vapor  would  be  uniformly  distributed  in  all  parts, 
there  would  be  everywhere  the  same  density,  and  a  perfect 
calm  in  the  atmosphere  would  exist  over  all  parts  of  the  globe. 
The  great  disturber  of  uniformity  of  temperature  on  the  earth's 
surface  is  the  unequal  distribution  of  the  sun's  radiated  heat. 
This  gives  rise  not  only  to  differences  of  temperature,  but  also 
to  differences  in  the  amount  of  aqueous  vapor,  in  the  air,  from 
both  of  which  causes  the  density  of  the  atmosphere  differs  in 
different  places,  and  thus  atmospheric  currents  are  produced. 
The  forces,  therefore,  which  overcome  the  inertia  of  the  atmos- 
phere when  at  rest  and  set  it  in  motion,  and  which  overcome 

the  frictional  and  other  resistances  and  maintain  this  motion 

» 

depend  upon  solar  heat  energy. 

Before  entering  upon  the  subject  of  the  general  circulation 
of  the  atmosphere — which,  we  have  seen,  is  exceedingly  elastic 
and,  so  far  as  we  know,  has  no  definite  superior  limit  or  surface 
— it  will  be  best  to  consider  a  few  simpler  cases  of  the  motions 
of  inelastic  fluids. 

If  any  kind  of  liquid  in  a  canal,  or  reservoir  of  any  kind,  or 
the  ocean  covering  the  greater  part  of  the  earth,  had  the  same 
density  in  all  parts  and  were  at  rest,  the  surface  of  the  liquid 
in  this  case  would  be  everywhere  perpendicular  to  the  direction 
of  the  force  of  gravity,  and  consequently  coincide  with,  or  be 
parallel  to,  the  spheroidal  surface  of  the  earth,  and  the  pres- 
sures in  a  horizontal  direction  on  each  side  of  any  part  of  the 
fluid  would  be  exactly  equal,  so  that  it  would  have  no  ten- 

89 


go      THE    GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

dency  to  move  in  any  direction.  But  if,  from  any  cause,  the- 
fluid  is  so  disturbed  that  its  surface  is  not  a  level  surface,  then 
the  pressure  of  the  fluid  beneath,  at  different  points  of  the 
same  level,  is  different,  and  horizontal  motion  takes  place  in 
the  direction  of  least  pressure.  From  the  nature  of  a  fluid  the 
pressure  at  any  point  is  equal  in  all  directions,  and  is  not  in  the 
direction,  only,  in  which  the  force  acts,  as  in  the  case  of  a 
.solid. 

62.  If  the  fluid  has  the  same  density  in  all  parts,  but  is  so 
disturbed,  from  some  cause,  from  its  state  of  static  equilib- 
rium, that  its  surface  is  not  a  level  surface,  then  the  fluid  at  all 
depths  has  the  same  tendency  to  flow  toward  the  lowest  sur- 
face level.  Let  ABCD,  Fig.  I,  represent  a  part  of  a  longi- 
tudinal and  vertical  section  of  a  canal,  and  abed  that  of  a 
cubic  unit  of  the  fluid — a  cubic  centimeter  or  a  cubic  inch,  for 
instance ;  then  the  pressure  on  each  point  of  the  vertical  sides 


of  the  cube  is  proportional  to  the  depth  of  the  point  below 
the  surface,  and  the  pressure  on  any  one  side  is  equal  to  the 
sum  of  the  pressures  upon  all  the  differential  elements  of  the 
surface.  If  we  draw  the  line  C ' D'  parallel  to  CD,  it  will  rep- 
resent a  line  in  a  plane  parallel  to  that  of  the  surface,  and 
hence  every  point  in  this  plane  will  be  subject  to  the  same 
pressure.  The  differences  of  these  pressures,  therefore,  upon 
all  the  differential  elements  on  the  same  level  of  the  sides  of 
the  cube  in  the  directions  of  greatest  and  least  pressure  are 
equal  to  the  vertical  pressure  of  a  column  of  fluid  of  the  same 
infinitely  small  base  and  altitude  de,  since  this  is  the  differ- 
ence of  depth  below  the  line  of  equal  pressure  CD'  between 
the  corresponding  differential  elements  of  the  two  sides  at  the 
same  depth.  The  difference  of  pressure,  therefore,  upon  the 


INTRODUCTION.  91: 

two  sides  of  the  cube  in  the  direction  of  greatest  and  least 
pressure  is  equal  to  the  vertical  pressure  of  a  stratum  of  fluid 
of  unit  base  and  depth  de.  But  the  pressure  of  the  whole  cube 
in  the  direction  of  the  force  of  gravity  is  to  that  of  the  thin 
stratum  of  the  same  base  as  their  respective  altitudes,  that  is, 
as  cd  or  ad  to  de.  The  force,  therefore,  which  tends  to  move 
the  cube  horizontally  in  the  direction  of  least  pressure,  and 
which  is  the  difference  of  the  pressures  on  the  two  sides,  is  to 
the  force  of  gravity  of  this  cube  as  de  to  ad\  and  hence  we 
have  the  force  which  tends  to  move  a  cube  of  unit  mass  hori- 
zontally in  the  direction  of  least  pressure  equal  to  g(de/ad\  or 
to  g  tan  dae.  But  tan  dae  is  the  change  of  level  in  the  hori- 
zontal distance  of  unity,  or  gradient  of  the  inclined  surface, 
which  we  have  denoted  by  e9  §  38.  The  horizontal  force, 
therefore,  for  unit  mass,  becomes,  as  in  §  38,  ge^  and  it  is  evi- 
dent that  this  is  the  same  for  all  depths,  since  the  preceding 
reasoning  is  entirely  independent  of  the  depth  at  which  the 
line  CD'  is  drawn. 

The  horizontal  force  in  this  case  being  the  same  at  all  depths,, 
the  fluid  at  all  depths  in  the  canal  has  the  same  tendency  to 
move  in  the  direction  of  least  pressure,  and  in  the  case  of  no 
resistances  from  the  bottom  or  sides,  all  parts  in  the  same  ver- 
tical line  would  acquire  the  same  velocity  of  horizontal  motion 
in  a  given  time,  and  this  would  be  accelerated  until  the  sur- 
face gradient  would  vanish  and  become  reversed,  after  which 
the  force  arising  from  the  reversed  gradient  would  gradually- 
overcome  the  momentum  and  stop  motion  in  that  direction, 
and  then  cause  a  reverse  motion.  Thus  an  oscillatory  motion 
would  be  produced,  which  in  the  case  of  no  friction  would 
never  stop,  but  which  in  the  case  of  friction  is  generally  of 
short  duration.  If  the  surface  of  this  fluid  and  all  isobaric 
surfaces  are  perfectly  horizontal,  then  de,  Fig.  I,  vanishes,  and 
also  the  quotient  e,  and  hence,  also,  the  force  ge  at  all  depths. 
There  are,  therefore,  no  forces  then  to  give  rise  to  and  main- 
tain motions,  and  the  fluid  remains  at  rest. 

63.  If  different  parts  of  the  fluid  of  a  canal  or  reservoir 
have  different  densities,  there  can  be  no  static  equilibrium  of. 


92      THE    GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

the  forces  arising  from  gravity  with  any  arrangement  of  the 
fluid,  as  long  as  the  differences  of  density  remain,  but  the 
forces  give  rise  to,  and  maintain,  a  system  of  counter  currents, 
which,  however,  tend  to  equalize  the  differences  of  densities 
unless  they  are  being  continually  reproduced  from  some  cause. 
The  differences  of  density  are  usually  caused,  either  directly 
or  indirectly,  by  differences  of  temperature.  Since  heat  ex- 
pands all  fluids,  if  different  parts  have  different  temperatures 
they  are  expanded  unequally ;  and  as  density  is  inversely  as 
the  volume  of  the  same  unit  of  mass,  the  more  the  fluid  is 
expanded  by  heat,  the  lighter  any  given  volume  of  it  becomes. 
Let  us  consider  here  the  simple  case  only  of  a  canal  or  trough 
•of  definite  length  and  of  uniform  depth.  If  all  parts  have  the 
same  temperature,  and  consequently  the  same  density,  we 
have  seen  that  if  the  surface  is  perfectly  level,  all  the  isobaric 
-surfaces  are  level,  and  there  is  no  tendency  in  any  part  of  it  to 
flow  in  any  direction,  and  the  whole  fluid  remains  at  rest.  If, 
however,  one  end  of  the  canal  has  a  greater  temperature  than 
the  other,  with  such  a  distribution,  let  us  suppose,  that  there 
is  a  uniform  temperature  gradient  from  one  end  to  the  other, 
and  has  also  the  same  temperatures  at  all  depths  of  the  same 
•parts  of  the  canal,  then  the  fluid  of  the  warmer  end  is  expanded 
more  than  that  of  the  other  end,  and  its  surface  and  each 
of  the  isobaric  planes  which  were  level  before  expansion  are 
raised  up  at  one  end  so  as  to  become  inclined  planes,  and  the 
inclination  is  greater  in  proportion  to  the  height  of  the  plane 
above  the  bottom.  There  is,  consequently,  a  tendency  in  the 
fluid  to  flow  down  the  inclined  planes  toward  the  colder  end ; 
but  this  tendency  is  not  the  same  at  all  depths,  as  in  the  pre- 
vious case  of  a  disturbance  of  level  but  not  of  density,  but  is 
greatest  at  the  top  and  gradually  decreases  downward,  being 
'in  proportion  to  the  height  above,  and  vanishing  at,  the  bot- 
tom. The  mere  upward  expansion  of  the  fluid  at  the  warmer 
end,  before  any  horizontal  motion  ensues,  does  not  affect  the 
pressure  at  the  bottom,  and  there  is  still  a  uniform  pressure 
there  from  one  end  to  the  other,  and  consequently  no  force 
vthere  to  move  the  fluid  in  either  direction.  As  the  upper  part 


IN  TROD  UCTIOiV. 


93. 


of  the  fluid,  however,  begins  to  flow,  it  fills  up  a  little  the  other 
end  and  raises  its  level  and  increases  the  pressure  there  on  the 
bottom,  while  the  level  at  the  warmer  end  is  depressed  a  little 
and  the  pressure  at  the  bottom  decreased  ;  so  that  there  is 
now  at  the  bottom  and  in  the  lower  strata  a  gradient  of  pres- 
sure decreasing  from  the  colder  to  the  warmer  end,  and  a 
tendency  in  the  fluid  there  to  flow  in  that  direction,  and  thus, 
to  give  rise  to  a  counter  current  in  the  lower  strata.  After 
this  has  taken  place  the  arrangement  of  the  isobaric  surfaces, 
represented  by  the  nearly  horizontal  lines,  and  the  motions  of 
the  fluid,  are  somewhat  as  represented  in  Fig.  2,  according  to 
which  these  surfaces  decline  from  the  warmer  to  the  colder 
end  of  the  canal  in  the  upper  strata  of  the  fluid,  and  reversely 
below,  and  in  consequence  of  which  the  fluid  flows  in  counter 
directions  above  and  below  a  given  neutral  intermediate  plane 


D 

d 


b  ** 

Fig.  2. 

of  equal  pressure,  ced,  in  which,  being  horizontal,  there1  is  no- 
pressure  gradient,  and  consequently  no  tendency  in  the  fluid 
to  move  in  either  direction.  In  the  upper  strata  the  greatest 
velocity  is  at  the  surface,  and  this  gradually  becomes  smaller 
with  increase  of  depth  below  the  surface  until  the  neutral 
plane  is  reached,  when  the  velocity  vanishes  and  changes  di- 
rection, and  then  increases  with  increase  of  depth  below  the 
surface ;  but  in  the  case  of  friction  between  the  fluid  and  the 
bottom  of  the  canal,  this  velocity  at  a  certain  depth  before  the 
bottom  is  reached  has  its  maximum,  and  then  decreases  again,, 
and  is  least  at  the  bottom. 

64.  In  the  motions  of  fluids  the  condition  must  be  satisfied 
that  no  more  of  the  fluid  shall  pass  into  any  given  space  than 
flows  out  of  it  in  a  given  time  where  there  is  no*  change  of 
density,  or  more  flow  out  than  flows  into  it ;  for  in  the  former 


'94      THE   GENERAL    CIRCULATION  OF   THE  ATMOSPHERE, 

case  the  density  would  be  necessarily  increased,  and  in  the  lat- 
ter diminished,  or  a  partial  vacuum  produced.  This  is  called 
.the  condition  of  continuity.  In  the  counter  motions  of  the  canal 
this  condition  must  be  fulfilled,  and  this,  consequently,  after 
the  regular  motions  are  established  and  there  is  no  further 
change  of  surface  level,  requires  that  just  as  much  fluid  in  the 
counter  currents  must  pass  through  any  given  vertical  section 
bef  of  the  canal  in  the  one  direction  as  in  the  other. 

The  satisfying  of  the  condition  of  continuity  not  only  re- 
quires counter  horizontal  motions  in  the  canal,  but  likewise 
vertical  ones ;  so  that  there  must  be  a  gradual  settling  down  of 
the  fluid  toward  the  bottom  at  the  end  toward  which  the  cur- 
rents in  the  upper  strata  run,  and  a  rising  up  again  toward  the 
surface  at  the  other  end.  The  vertical  components  of  velocity, 
.at  least  in  a  shallow  canal,  are  extremely  small  in  comparison 
with  those  of  the  horizontal  motions,  and  are  not  indicated  in 
Fig.  2.  The  counter  vertical  motions  have  likewise  a  neutral 
plane,  a  vertical  one,  bef,  somewhere  in  the  middle  part  of 
the  canal,  separating  the  part  of  the  fluid  which,  at  any  time, 
has  a  slight  downward  tendency  from  that  on  the  other  side 
which  is  slowly  rising  toward  the  surface  ;  and  with  reference 
to  this  plane  the  condition  must  likewise  be  satisfied  that  just 
.as  much  of  the  fluid  must  slowly  descend  on  the  one  side  to- 
ward the  bottom,  through  any  given  horizontal  section  of  the 
>canal  as  that  represented  by  det  as  rises  up  on  the  other  side 
of  it  toward  the  surface,  through  the  corresponding  section  ce 
at  the  same  depth.  If  the  canal  or  trough,  therefore,  were 
wedge-shaped,  or  had  any  shape  which  would  make  it  narrower 
toward  the  one  end  than  the  other,  the  vertical  section  divid- 
ing the  very  slowly  moving  vertical  counter  currents,  would 
have  to  be  nearer  the  wide  end  so  that  the  horizontal  sectional 
.areas  of  these  counter  vertical  currents  might  be  equal,  or 
nearly  so. 

65.  If  there  were  no  frictional  resistances  to  the  counter 
motions,  th$  tendency  of  the  pressure  gradients,  in  the  one  di- 
rection above  and  the  contrary  below,  would  be  to  cause  a 
continued  acceleration  of  these  motions;  but  as  there  are  al- 


INTRODUCTION  95 

ways  resistances  of  this  kind,  the  motions  are  only  accelerated 
until  the  frictional  resistances  become  equal  to  the  forces  caus- 
ing'and  maintaining  the  motions,  after  which  the  whole  of  the 
forces  is  spent  in  overcoming  the  resistances,  and  there  is  no 
further  acceleration. 

In  case  of  friction  between  the  horizontal  strata,  but  none 
between  the  fluid  and  the  bottom  of  the  canal,  the  velocities 
of  the  counter  horizontal  currents  must  increase  from  the  hor- 
izontal neutral  plane  both  toward  the  top  and  the  bottom, 
where  they  are,  consequently,  the  greatest.  The  relative  ve- 
locities, however,  between  the  strata  must  decrease  from  this 
neutral  plane  both  upward  and  downward,  and  be  least  at  the 
top  and  bottom.  The  forces  arising  from  the  pressure  gra- 
dients which  cause  the  counter  motions  act  on  all  the  strata, 
but  most  upon  the  upper  and  bottom  strata,  since  here  the 
gradients  are  greatest.  The  action  of  the  force  upon  the 
first  stratum  increases  the  relative  velocity  between  this  stra- 
tum and  the  next  until  the  frictional  resistance  is  equal  to  the 
force.  This  force,  by  means  of  friction,  is  communicated  to 
the  second  stratum,  so  that  the  force  overcoming  the  frictional 
resistance  between  the  second  and  third  stratum  is  equal  to 
the  sum  of  the  forces  acting  upon  the  first  two  strata,  and  con- 
sequently the  relative  velocity  between  the  second  and  third  is 
greater  than  that  between  the  first  and  second.  So  the  force 
overcoming  the  resistance  between  the  third  and  fourth  is 
equal  to  the  sum  of  the  forces  acting  upon  the  first  three 
strata,  and  so  on.  The  relative  velocities  between  the  strata 
must  therefore  increase  from  the  surface  down  to  the  neutral 
plane  where  the  forces  vanish.  But  the  sums  of  these  forces 
are  not  proportional  to  the  depth,  since  the  gradients  and  the 
forces  gradually  decrease  down  to,  and  vanish  at,  the  neutral 
plane.  The  relative  velocities,  therefore,  at  and  near  this  neu- 
tral plane  are  greatest  and  vary  very  slowly  near,  and  are  least 
at,  the  top.  The  same  would  be  the  case  commencing  at  the 
bottom,  if  there  were  no  friction  between  the  bottom  of  the 
canal  and  the  lower  stratum,  so  that  this  would  be  as  free  to 
move  from  the  force  acting  upon  it  as  the  upper  stratum,  and 


96      THE    GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

the  actual  velocities  would  be  greatest  and  the  relative  veloci- 
ties least  at  the  bottom. 

When  the  lower  stratum  suffers  resistance  from  the  bottom 
the  velocities  of  the  strata  near  the  bottom  increase  up  to 
some  intermediate  stratum  between  the  bottom  and  the  neu- 
tral plane,  and  then  decrease  up  to  this  plane,  where  they  van- 
ish and  become  reversed  in  direction.  In  this  case  the  resist- 
ances to  the  motions  of  the  strata  between  the  neutral  plane 
and  the  bottom,  if  there  is  the  same  amount  of  flow  through 
equal  sectional  areas,  are  much  greater  than  they  are  in  the 
strata  above  this  plane,  since  in  the  one  case  the  flow  is  re- 
sisted through  friction  both  by  the  bottom  of  the  canal  and 
the  neutral  stratum,  while  in  the  other  it  is  resisted  by  the  one 
only,  the  neutral  stratum.  In  order,  therefore,  that  the  condi- 
tion of  continuity  may  be  satisfied  in  the  case  of  friction  on  the 
bottom,  there  must  be  either  a  greater  force,  or  a  greater  ver- 
tical sectional  area  for  the  fluid  to  pass  through,  or  both,  in  the 
lower  current ;  and  both  of  these  are  brought  about  by  an  ele- 
vation of  the  horizontal  neutral  plane,  that  is,  by  a  greater  fill- 
ing up  and  raising  up  of  the  surface  of  the  colder  end  of  the 
canal,  which  both  makes  the  sectional  area  and  the  pressure 
gradients  of  the  lower  one  of  the  counter  currents  greater  in 
comparison  with  those  of  the  upper  one.  There  is  then  a 
slower  motion  through  a  greater  sectional  area  in  the  lower 
current  and  a  comparatively  rapid  one  of  smaller  sectional  area 
in  the  upper  one,  and  the  velocity  is  especially  much  greater 
near  the  surface. 

66.  The  interchanging  horizontal  motions  of  the  fluid  be- 
tween the  two  ends  of  the  canal  are  oscillatory.  The  motion 
of  any  particle  of  the  fluid  starting  from  its  extreme  position 
in  the  warmer  end  and  upper  strata  of  the  canal  is  first  accel- 
erated until  the  middle  part  is  reached,  after  which  it  is  gradu- 
ally retarded  until  the  particle  is  brought  to  rest  in  its  extreme 
position  toward  the  other  end,  where,  gradually  settling  down 
toward  the  bottom,  its  motion  is  first  accelerated  again,  and 
after  passing  its  middle  position  it  is  then  gradually  retarded, 
and  at  the  same  time  rises  up  into  the  upper  strata  whence  it 


INTRODUCTION.  97 

started.  Thus  a  particle  describes  a  very  elongated  elliptic 
orbit,  in  which,  especially  in  shallow  and  long  canals,  the  trans- 
verse axis  is  very  small  in  comparison  with  the  other.  The 
major  axes  also  are  very  different  for  different  particles,  those 
near  the  top  and  bottom  passing  nearly  or  quite  to  the  ends  of 
the  canal,  while  those  near  the  central  part  and  at  medium 
depth  make  only  short  excursions  on  either  side  of  the  neutral 
vertical  plane  bef,  Fig.  2.  If,  however,  there  are  any  ab- 
normal disturbances,  however  small,  besides  that  arising  from 
the  regular  temperature  gradient,  or  any  irregularities  in  the 
bottom  or  sides  of  the  canal,  there  is  an  interchanging  and 
mixing  up  of  the  particles,  so  that  the  same  one  does  not  con- 
tinue in  the  same  regular  orbit. 

67.  In  the  case  of  the  open  ocean  extending  from  the 
equator  to  the  pole,  we  can  consider  alone  any  part  included 
between  two  meridians  meeting  at  the  pole,  and  this  half-lune 
is  similar  to  the  wedge-shaped  trough  except  that  it  does  not 
become  narrow  so  rapidly  near  the  equator,  and  only  becomes 
reduced  to  half  its  equatorial  width  on  the  parallel  of  60°, 
which  is  two  thirds  of  the  distance  from  the  equator  to  the 
pole.  If  we  suppose  that  there  is  a  uniform  temperature  gra- 
dient at  all  depths  between  the  equator  and  the  pole,  the  in- 
terchanging motion  for  any  such  half-lune  would  be  somewhat 
as  in  the  case  of  the  wedge-shaped  trough.  There  would  be  a 
more  rapid  motion  in  the  upper  current  of  smaller  sectional 
area,  and  a  comparatively  slow  one  in  the  lower  counter  cur- 
rent with  large  sectional  area ;  so  that  the  neutral  plane  be- 
tween the  counter  currents  would  be  at  no  great  depth  below 
the  surface.  The  vertical  section,  also,  between  the  parts  hav- 
ing a  slow  descent  toward  the  bottom  in  the  polar  region  and 
those  slowly  rising  toward  the  surface  in  the  equatorial  region 
would  not  be  on  the  parallel  of  45°,  but  somewhere  near  the 
parallel  of  30°,  so  as  to  make  the  horizontal  sectional  areas  of 
both  parts  about  equal. 


98      THE    GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 


DISTRIBUTION  OF  TEMPERATURE  OVER  THE  EARTH'S  SURFACE. 

68.  Since  the  motions  of  the  atmosphere  depend  upon  dif- 
ferences of  temperature,  it  is  necessary  to  know  at  the  outset, 
in  the  investigation  of  these  motions,  the  distribution  of  tem- 
perature over  the  earth's  surface,  not  only  for  the  mean  of  the 
year,  but  also  for  the  different  seasons  of  the  year.  Since  all 
parts  of  the  earth's  surface  on  the  same  parallels  of  latitude  have 
the  same  relation  to  the  sun,  upon  which  their  temperatures  and 
the  differences  of  temperature  depend,  if  the  whole  surface 
were  either  all  land  or  all  water,  and  perfectly  homogeneous, 
there  would  be  the  same  temperature  all  around  the  globe  on 
the  same  latitude,  and  there  would  be,  at  all  longitudes,  the 
same  temperature  gradient  between  the  equator  and  the  pole. 
In  the  case  of  a  wholly  land  surface,  however,  the  differ- 
ence of  temperature  between  the  equator  and  the  pole,  and 
consequently  the  temperature  gradient,  would  be  much  greater 
than  in  the  case  of  an  earth  entirely  covered  by  the  ocean. 
For  in  the  latter  case,  in  consequence  of  the  difference  of 
temperature  of  the  water  of  the  equatorial  and  the  polar 
regions,  there  are  interchanging  counter  currents,  as  just  ex- 
plained, by  which  heat  is  conveyed  from  the  former  to  the 
latter  region,  the  effect  of  which  is  to  make  the  difference  of 
temperature  between  the  two  regions  much  less  than  it  other- 
wise would  be,  and  consequently  to  diminish  the  temperature 
gradient  between  the  equator  and  the  poles.  In  the  case  of 
the  earth,  therefore,  as  really  constituted,  with  continents  and 
oceans  extending  from  the  equator  to  the  pole,  or  nearly  so, 
the  temperature  gradients  between  the  equator  and  the  pole 
on  the  continents  are  somewhat  as  they  would  be  in  case  of  a 
wholly  land  surface,  while  on  the  oceans  they  are  somewhat  as 
on  an  earth  entirely  covered  by  the  ocean,  and  consequently 
the  temperature  gradients  on  the  former  are  greater  than  on 
the  latter.  For  this  reason  the  equatorial  and  tropical  parts  of 
the  continents  are  warmer  than  those  of  the  ocean,  while  the 
reverse  is  true  in  the  higher  latitudes,  and  hence  there  are 


'DISTRIBUTION  OF    TEMPERATURE   OVER   THE  EARTH.   99 


Differences  of   temperature  on  the  same  latitude   in  different 
longitudes. 

In  the  general  circulation  of  the  atmosphere  all  the  second- 
ary and  abnormal  irregularities  are  neglected,  and  only  the 
normal  and  principal  temperature  inequality,  determined  by 
the  averages  of  temperature  of  each  latitude,  taken  all  around 
the  globe,  is  considered.  These  averages  of  temperature  are 
called  the  normal  temperatures  of  the  latitude.  These  normals  of 
temperature,  taken  from  "  Meteorological  Researches,"  Part  I,8 
for  the  average  of  the  year,  and  also  for  the  two  months  of  ex- 
treme temperatures,  are  given  for  each  tenth  degree  of  latitude 
in  the  following  table  : 


LATITUDE. 

JANUARY. 

JULY. 

MEAN  OF  THE  YEAR. 

•°C. 

OF. 

°C. 

0  F. 

°C. 

r  . 

+  80 

-31-9 

-25.4 

+  1.0 

+  33.8 

—  15-5 

+  4-1 

70 

26.5 

15.7 

6.9 

44.4 

9.8 

14.4 

60 

l6!g 

-1.6 

I3-8 

56.8 

-1.6 

29.1 

50 

-6.0 

-f-21.2      ' 

18.6 

65.5 

+  6.3 

43-3 

40 

+  4-5 

40.1 

22.8 

73-0 

13-6 

56-5 

30 

12.9 

55-2 

26.6 

79-9 

19.8 

67.6 

20 

21.7 

71.1 

29.0 

84.2 

25.3 

77-5 

-f  10 

25-9 

78,6 

28.4 

83.1 

27.2 

81.0 

O 

27-3 

Bi.l 

26.1 

79.0 

26.7 

80.  i 

—  10 

27-9 

82.2 

24.0 

75-2 

25-9 

78.6 

20 

26.6 

79-9 

20.8 

69.4 

23-7 

74-7 

30 

23-0 

73-4 

15.6 

60.  i 

19-3 

66.7 

40 

17.6 

63.7 

II.  I 

52.0 

14.4 

57-9 

50 

ii.  I 

52.0 

+  6.4 

43-5 

8.8 

47-8 

-60 

+  3-6 

+  38.5 

0.0 

+  32.0 

+  1.8 

+  35.2 

It  is  seen  from  this  table  that,  while  the  temperatures  at 
and  near  the  equator  are  very  nearly  the  same  the  year  around, 
in  the  higher  latitudes  of  the  northern  hemisphere  they  vary 
very  much  in  the  different  seasons  of  the  year,  and  that  the 
temperature  gradients  between  the  equator  and  the  pole  are 
more  than  twice  as  great  in  midwinter  as  in  midsummer.  In 
the  southern  hemisphere,  however,  these  annual  variations  are 
•comparatively  very  small.  This  is  because  nearly  all  the  land 
lies  in  the  northern  hemisphere  and  the  southern  hemisphere 


IOO  THE   GENERAL    CIRCULATION  OF   THE  ATMOSPHERE.. 

is  mostly  covered  by  the  ocean,  which  equalizes  somewhat  the 
extreme  temperatures  of  the  seasons. 

On  account  of  the  interchange  of  equatorial  and  polar 
waters  in  nearly  every  part  of  the  southern  hemisphere,  while 
this  in  the  northern  hemisphere  takes  place  over  a  much 
smaller  part,  since  much  less  of  it  is  covered  by  the  ocean,  the 
normal  temperatures  of  latitude  for  the  average  of  the  year  in 
the  southern  hemisphere  are  a  little  less  in  the  lower,  and  a 
little  greater  in  the  higher,  latitudes  than  on  the  corresponding 
latitudes  of  the  northern  hemisphere.  This  causes  the  maxi- 
mum of  temperature  or  thermal  equator  to  fall  a  little  north  of 
the  equator. 

The  normals  of  latitude  in  the  preceding  table  were  ob- 
tained from  Buchan's  isothermal  charts.  According  to  later 
researches  of  Dr.  Hann,9  in  which  are  used  observations  on 
high  southern  latitudes  more  recent  than  any  used  by  Buchan, 
and  the  tabular  means  and  normals  of  temperature  given  by 
Herr  Spitaler,  deduced  from  Dr.  Hann's  recent  isothermal 
charts,  the  normals  of  temperature  in  these  latitudes  are 
somewhat  less  than  those  given  in  the  preceding  table.  Al- 
though the  disturbing  forces  which  we  are  to  consider  in  the 
motions  of  the  atmosphere  do  not  depend  upon  the  abso- 
lute average  temperature  of  the  globe  but  upon  differences 
of  temperature  or  temperature  gradients,  yet  it  may  not  be 
amiss  to  state  here,  as  a  matter  of  general  interest,  that  the 
average  temperature  of  the  atmosphere  at  the  earth's  surface, 
taken  over  the  whole  of  the  northern  hemisphere,  is  15°. 3 
(59°. 5  F.),  and  that  that  of  the  southern  hemisphere  is  sensibly 
the  same. 

69.  It  must  not  be  understood  that  the  preceding  normals 
are  those  of  the  whole  atmosphere  extending  to  the  top,  but 
simply  those  of  the  part  in  contact  with  the  earth's  surface,  for 
the  temperature  everywhere  decreases  with  increase  of  altitude. 
The  rate  of  this  decrease,  on  the  average  for  all  latitudes  and  all 
seasons  of  the  year,  is,  for  the  lower  half  of  the  atmosphere, 
about  o°.65  for  each  100  meters  of  ascent ;  or,  in  English  meas- 
ures, o°.36  for  each  100  feet.  This  rate  is  supposed  to  be  a  little 


DISTRIBUTION  OF  AQUEOUS    VAPOR.  IOI 

greater  in  the  lower  than  in  the  higher  latitudes,  but  the  differ- 
ence is  small,  and  it  is  also  greater  in  general  in  summer  than  in 
•winter,  and  by  day  than  by  night,  and  this  is  especially  the  case 
on  land  and  in  the  lower  part  of  the  atmosphere.  The  varia- 
tion of  temperature  with  altitude,  however,  so  long  as  the 
unstable  state  is  not  induced,  is  of  little  importance  in  the  dy- 
namics of  the  atmosphere,  since  the  forces  depend  not  upon 
absolute  temperatures,  but  upon  the  horizontal  temperature 
gradients,  and  these,  so  far  as  they  pertain  to  the  general  circu- 
lation, are  very  nearly  the  same  at  all  altitudes. 

DISTRIBUTION   OF  AQUEOUS  VAPOR. 

70.  Since  aqueous  vapor  under  the  same  pressure  is  lighter 
than  air,  its  density  being  to  that  of  air  as  0.622  to  I,  the  un- 
equal distribution  of  this  vapor  in  the  atmosphere  also  gives 
rise  to  small  differences  of  normal  pressure  in  different  lati- 
tudes, or,  in  other  words,  to  pressure  gradients  between  the 
equatorial  and  polar  regions,  but  these  are  small  in  comparison 
with  those  arising  from  difference  of  temperature.  It  is  seen 
from  Table  II,  Appendix,  that  the  greatest  vapor  tension 
which  can  exist  in  the  atmosphere  at  the  equator  with  a  tem- 
perature, say,  of  26°,  is  about  25  mm.  ;  while  for  the  cold  tem- 
perature of  the  polar  regions  at  a  temperature  of  —  15°  the 
tension  of  saturation  is  almost  nothing.  As  the  relative  hu- 
midity of  the  atmosphere  at  all  places  and  all  seasons  of  the 
year  is  about  80  per  cent,  this  gives  25  X  0.80  =  20  mm.  for 
the  average  vapor  tension  at  the  equator.  This  is  the  1/38 
part  of  760  mm.,  the  normal  barometric  pressure  of  the  atmos- 
phere. The  density  of  the  aqueous  vapor  being  0.622,  the 
density  of  the  part  of  the  atmosphere  comprising  the  aqueous 
vapor  is  diminished  by  I  — 0.622  =0.378,  and  this  multiplied 
into  1/38  gives  a  decrease  of  the  density  of  the  whole  atmos- 
phere equal  to  i/ioo  part.  This  is  equal  to  the  diminution  of 
density  arising  from  an  increase  of  temperature  of  2°. 7.  Hence 
the  effect  of  the  average  amount  of  aqueous  vapor  in  the  at- 
mosphere at  the  equator  on  its  density  is  about  the  same  as 


102   THE    GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

that  of  increasing  its  temperature  2°. 7,  or  about  the  one-tenth 
part.  This  is  the  proportion  of  increase  of  the  numerical  co- 
efficient of  temperature  which  Laplace  introduced  into  his  baro- 
metric formula  in  order  to  take  into  account  approximately 
the  effect  of  the  average  amount  of  aqueous  vapor  in  the  at- 
mosphere. Although  this  proportion  is  very  nearly  correct 
for  equatorial  temperatures  at  and  near  the  earth's  surface,  yet 
it  becomes  erroneous  for  temperatures  at  and  below  the  zero* 
of  the  Centigrade  scale  ;  but  at  these  temperatures  the  absolute 
amount  of  vapor  is  so  small  that  the  erroneous  proportion 
gives  rise  to  only  very  small  errors.  In  all  cases,  therefore,  we 
may  assume,  that  for  the  average  or  normal  state  of  the  atmos- 
phere the  modifying  effect  of  the  aqueous  vapor  is  such  as  to 
cause  the  atmosphere  to  expand  its  volume  and  diminish  its 
density  about  the  1/250  instead  of  the  1/273  part,  for  each 
degree  of  increase  of  temperature.  But  this  is  the  case  in  the 
lower  part  only  of  the  atmosphere.  In  the  upper  regions  of 
the  atmosphere  the  proportion  of  vapor  in  the  atmosphere  is 
less,  both  on  account  of  the  diminished  temperature  with  in- 
crease of  altitude,  and  also  because  evaporation  takes  place  at 
the  earth's  surface  and  the  vapor  is  very  slowly  diffused  upward 
to  high  altitudes.  The  decrease  of  density,  therefore,  from  this 
cause,  at  high  altitudes,  and  the  corresponding  effect  upon  the 
pressure  gradients  between  the  equator  and  the  pole,  are  small 
in  comparison  with  those  arising  directly  from  differences  of 
temperature.  Upon  the  whole,  therefore,  considering  the 
whole  depth  of  the  atmosphere,  the  effect  of  the  aqueous 
vapor  is  small,  but  even  this  depends  indirectly  upon  difference 
of  temperature,  since  without  this  there  would  be  no  difference 
in  the  amount  of  the  vapor  in  the  equatorial  and  the  polar 
regions. 

GENERAL  CIRCULATION  WITHOUT  ROTATION  OF  THE  EARTH. 

71.  In  treating  the  general  circulation  of  the  atmosphere, 
it  will  be  best  to  consider  first,  in  a  preliminary  way,  the  more 
simple  case  of  circulation  without  rotation  of  the  earth  on  its 


CIRCULATION    WITHOUT  ROTATION  OF   THE  EARTH.   1 03 

axis.  For  although  this  is  not  the  real  case  of  nature,  yet  the 
results  obtained  in  this  case  will  be  useful  and  necessary  in 
treating  the  more  general  and  more  complex  case  in  which  the 
earth  turns  on  its  axis.  Let  PCE,  Fig.  3,  represent  a  quadrant 
of  a  meridional  section  of  the  earth,  and  oaf,  bbr ,  cc' ,  etc.,  repre- 
sent infinitely  thin  strata  of  the  atmosphere  of  equal  pressure  in 
case  all  parts  had  the  temperature  of  the  pole  P.  In  this  case 
these  strata  would  all  be  horizontal  or  equidistant  from  the 
earth's  surface  and  from  one  another  at  the  equator  and  at  the 
poles,  neglecting  quantities  of  the  order  of  the  earth's  ellipticity, 
which  are  of  no  importance  here.  But  by  the  preceding  table, 


Fig.  3. 

§  68,  the  temperature  of  the  atmosphere  at  the  earth's  surface 
is  about  45°  C.  greater  at  the  equator  than  at  the  poles;  and 
in  the  upper  strata,  we  have  reason  to  think,  the  difference  is 
nearly  the  same.  The  effect  of  increase  of  temperature  being  to 
expand  the  air  the  1/273  part  of  its  volume  at  the  temperature 
of  melting  ice  for  each  degree  of  its  increase,  the  effect  of  an 
increase  of  temperature  of  45°  at  the  equator  is  to  expand  the 
air  upward  the  45/273  or  1/6  part  nearly  of  its  volume  at  this 
temperature,  but  a  little  more  than  this  part  of  its  volume  at 
the  temperature  of  the  poles.  The  stratum  aa'  is  accordingly 
elevated  at  the  equator  about  1/6  of  the  altitude  Ed  of  this 
stratum  above  the  earth's  surface,  that  of  bb'  by  1/6  of  Eb' ,  and 
that  of  cc'  by  1/6  of  EC',  and  so  on  ;  each  successive  stratum 


104   THE    GENERAL    CIRCULATION   OF   THE  ATMOSPHERE. 

being  raised  in  proportion  to  its  altitude  above  the  earth's  sur- 
face, and  the  new  positions  of  the  strata,  resulting  from  such 
an  increase  of  temperature  as  given  in  the  preceding1  table,  and 
consequently  the  upward  expansions,  are  somewhat  as  repre- 
sented by  the  dotted  lines  in  the  figure. 

If  this  increase  of  the  temperature  of  the  equatorial  over 
that  of  the  polar  regions  were  made  instantaneously,  the  first 
effect  of  the  expansion  would  be  to  cause  gradients  down 
which  the  air  of  the  upper  strata  would  tend  to  flow  from  the 
equator  toward  the  poles, — just  as  in  the  case  of  the  canal,  §  62, 
the  upper  strata  have  a  tendency  to  flow  from  the  warmer 
toward  the  colder  end  ;  and  the  greater  the  altitude  above  the 
bottom  or  earth's  surface,  the  greater  is  this  tendency  in  both 
cases.  At  the  earth's  surface,  however,  there  would  be  no 
tendency  in  the  air  to  flow  either  from  or  toward  the  equator, 
since  the  mere  upward  expansion  would  not  affect  the  pressure 
at  the  earth's  surface,  and  thus  give  rise  to  a  pressure  gradient 
acting  in  either  direction. 

The  linear  gradient  e  of  any  isobaric  surface  at  the  altitude 
h,  due  to  difference  of  temperatures,  is  equal  to  the  difference 
of  upward  expansion  of  a  vertical  column  of  air  at  each  end  of 
a  unit  of  length  in  the  direction  in  which  the  gradient  is 
reckoned,  whatever  may  be  the  assumed  unit.  Putting,  there- 
fore, r,  and  r2  for  the  temperatures  at  the  beginning  and  end  of 
the  unit  respectively,  we  shall  have  the  upward  expansion  of 
the  former  equal  to  -^^/irl  and  that  of  the  latter  equal  to 
-s^hr^ ,  if  1i  is  the  height  of  the  column  at  the  temperature  of 
o°  C.,  since  the  volume  of  air  expands  the  -^-3  part  of  its 
volume  at  o°  C.,  for  each  degree  of  increase  of  temperature. 
Hence,  putting  AT:  (variation  of  r)  for  the  change  of  tempera- 
ture in  the  distance  of  unity,  or,  in  other  words,  for  this  tem- 
perature gradient,  we  shall  have 

e  = 

72.  The  first  effect  of  the  motion  in  the  upper  strata  of 
the  atmosphere  from  the  equator  toward  the  pole,  as  in  the 
case  of  the  water  flowing  from  the  warmer  toward  the  colder 


'CIRCULATION    WITHOUT  ROTATION  OF    THE   EARTH.   IO5 

*end  of  the  canal,  would  be  to  fill  up  a  little,  as  it  were,  the 
polar  region  with  air  from  the  equatorial,  the  effect  of  which  is 
to  increase  the  pressure  a  little  in  the  former  and  to  decrease 
it  a  little  in  the  latter  region,  thus  creating  at  the  earth's 
surface  and  in  the  lower  strata  a  gradient  of  pressure  decreas- 
ing from  the  pole  toward  the  equator,  which  would  cause  a 
-counter  current  in  the  lower  strata.  The  neutral  plane  where 
there  is  no  pressure  gradient,  and  consequently  no  motion  in 
either  direction,  is  now  raised  from  the  earth's  surface  up  to 
such  an  altitude  that  the  counter-flows  between  the  equator 
and  the  pole,  from  the  equator  above  and  toward  it  below, 
satisfy  the  condition  of  continuity,  and  this  altitude  must  be 
greater  or  less  according  to  the  relative  amounts  of  friction  in 
the  upper  and  lower  strata.  For  reasons  given  in  §  65  in  the 
-case  of  the  canal,  this  must  be  above  half  the  mass  of  the 
atmosphere.  Since  the  upper  part  of  the  atmosphere  has  no 
definite  limit,  but  becomes  more  and  more  rare  and  extends  to 
a  very  high  but  unknown  altitude,  the  isobaric  surfaces  of  the 
upper  very  rare  part  of  the  atmosphere  have  very  steep  gradi- 
ents, which  increase  in  proportion  to  the  altitude  above  the 
neutral  plane.  But  the  force  with  which  a  given  volume  of  air 
tends  to  slide  down  these  gradients  or  press  toward  the  pole  is 
as  the  density,  and  this,  where  the  temperature  remains  the 
same,  is  as  the  pressure.  While  the  gradients,  therefore, 
increase  with  increase  of  altitude  above  the  neutral  plane  in  an 
arithmetical  progression,  the  forces  for  the  same  gradient  de- 
crease with  increase  of  this  altitude  in  a  geometrical  progression, 
and  so  become  small  above,  while,  by  the  nature  of  gases,  §33, 
the  frictional  resistances  for  equal  relative  velocities  between 
the  strata  are  the  same  for  all  densities,  and  so  the  same  at  all 
.altitudes.  Hence  the  relative  velocities  between  the  strata,  in 
the  case  of  no  rotation  of  the  earth  on  its  axis,  would  be  very 
small  at  great  altitudes,  and  the  absolute  velocities  nearly  the 
same  at  all  high  altitudes. 

'  73.  The  whole  vertical  circulation  of  the  atmosphere  in  this 
case  would  be  similar  to  that  of  the  water  of  the  canal,  §  66, 
the  particles  of  air  would  have  an  oscillatory  horizontal  and 


IO6   THE   GENERAL    CIRCULATION   OF    THE  ATMOSPHERE. 

vertical  motion,  which  in  the  upper  strata  of  the  equatorial! 
region  is  first  accelerated  until  the  particle  arrives  at  some 
intermediate  latitude,  after  which  it  is  gradually  retarded  in  its 
further  motion  toward  the  pole  and  brought  to  rest  at  its  polar 
limit  of  range,  meanwhile  gradually  settling  down  toward  the 
earth's  surface,  where  the  pressure  gradient  is  reversed  and  the 
reversed  motion  of  the  particle  is  again  accelerated  until  it 
arrives  at  some  intermediate  latitude  of  its  range  of  oscillation,, 
after  which  it  is  again  retarded  in  its  horizontal  motion  and 
brought  to  rest,  meanwhile  rising  up  to  higher  altitudes,  where 
the  force  of  the  pressure  gradient  is  again  reversed,  and  it 
commences  again  another  circuit  as  before.  The  nearer  the 
particle  is  to  the  neutral  planes,  the  shorter  are  the  ranges  of 
oscillation,  both  horizontal  and  vertical,  and  the  smaller  the 
elliptic  circuit.  On  account  of  the  narrowing  of  the  spaces- 
between  the  meridians  in  approaching  the  pole,  the  vertical 
plane  between  the  descending  air  in  the  higher  latitudes  and 
ascending  air  in  the  lower  ones,  as  in  the  case  of  the  oceanic 
circulation,  cannot  be  half-way  from  the  equator  to  the  pole, 
but  must  be  about  the  parallel  of  30°. 

In  the  case  of  no  friction  the  motions  would  be  continually 
accelerated  as  long  as  any  difference  of  temperature  between 
the  equator  and  the  pole  remained,  but  of  course  a  very  rapid 
and  increasing  interchange  would  tend  to  diminish  and  finally 
to  sensibly  destroy  this  difference.  In  the  case  of  friction  the 
motions  would  be  accelerated  until  the  frictional  resistances 
would  be  equal  to  the  forces,  after  which  a  uniform  horizontal 
oscillatory  motion  would  be  maintained,  the  relation  between 
the  gradients  and  the  frictional  resistances  being  such  as  to 
leave  a  small  residual  force  to  alternately  accelerate  and  retard, 
the  motions  of  the  oscillations. 

GENERAL    CIRCULATION  WITH   ROTATION   OF   THE   EARTH 
ON   ITS   AXIS. 

74.  The  general  vertical  circulation  of  the  atmosphere 
which  would  take  place  in  case  the  earth  had  no  rotation  on  its- 
axis  having  just  been  explained,  we  come  now  to  consider  the 


CIRCULATION    WITH  EARTH  ROTATING   ON  ITS  AXIS.   IO? 

effect  upon  this  circulation  of  the  deflecting  force  arising  from 
the  earth's  rotation,  explained  in  the  preceding  chapter,  in  the 
real  case  of  nature.  In  consequence  of  this  force,  §  53,  in 
whatever  direction  any  part  of  the  atmosphere  may  be  moving,, 
it  is  continually  deflected,  if  free,  to  the  right  of  the  direction. 
of  motion  in  the  northern  hemisphere  and  the  contrary  in  the 
southern  ;  and  if  not  free,  it  presses  in  these  directions  and 
causes  atmospheric  gradients,  ascending  in  the  directions  of 
pressure.  Hence  the  vertical  circulation  due  to  the  real  forces 
arising  from  difference  of  temperature  between  the  equator  and 
the  poles  being  once  established,  the  air  in  the  upper  strata  of. 
the  atmosphere  in  either  hemisphere,  in  moving  toward  the. 
pole,  is  deflected  eastward,  and  in  the  counter  current  in  the 
lower  strata  the  tendency  is  to  counteract  and  destroy  motion 
toward  the  east  and  then  to  cause  a  west  component  of  motion. 
These  contrary  forces,  acting  toward  the  east  above  and  the 
west  below,  give  rise  to  relative  velocities  between  the  strata,. 
and  maintain  them  by  overcoming  the  friction  between  the. 
strata,  which  otherwise  would  constantly  tend  to  reduce  and 
to  destroy  these  relative  velocities,  and  to  reduce  the  absolute 
velocities  above  and  below  all  to  the  same  velocity  on  any  given, 
parallel  of  latitude. 

In  the  case  of  no  friction  between  the  air  and  the  earth's 
surface,  the  east  and  west  components  of  velocity  arising  from 
the  interchanging  motions  between  the  equatorial  and  polar 
regions  and  the  deflecting  forces  depending  upon  the  earth's 
rotation  arising  from  them,  would  satisfy  the  expression 


in  which  the  value  of  c  is  the  average  value  of  rw  for  all  the 
particles  of  the  air  of  the  hemisphere,  before  interchanging 
motion  took  place,  the  definitions  of  r  and  w  being  those  of 
§  47  ;  or  it  is  the  average  value  of  rnw0  ,  in  which  r0  and  w0  are. 
the  values  of  r  and  w  before  motion  commences  and  while 
the  air  is  at  rest  relative  to  the  earth's  surface,  in  which  case  w 
is  equal  to  rn.  If  each  particle  of  air  were  entirely  free,  both 
from  the  effect  of  friction  of  the  earth's  surface  and  the  inter- 


IO8    THE    GENERAL    CIRCULATION   OF    THE  ATMOSPHERE. 

action  of  the  particles  upon  each  other,  then  its  motions  would 
satisfy  the  equation  rw  =  r0wQ ,  and  since  in  the  interactions 
between  the  particles  action  and  reaction  are  equal,  these  can- 
not affect  the  average  value  of  rw  for  the  whole  hemisphere, 
and  it  must  remain  the  same  at  all  times  and  be  the  same  as 
before  motion  commenced,  that  is,  be  the  average  value  of  r0w0 
taken  for  the  whole  hemisphere. 

In  order  to  satisfy  the  preceding  relation  near  the  pole, 
where  r  is  small  w  must  be  very  large ;  and  this  here  becomes 
mostly  an  east  velocity  relative  to  the  earth's  surface,  since 
near  the  pole  the  part  depending  upon  the  earth's  rotation, 
rn,  is  small. 

In  consequence  of  friction  between  the  lower  stratum  of 
the  atmosphere  and  the  earth's  surface,  this  stratum,  with  the 
forces  only  being  here  considered,  cannot  have  either  an  east- 
erly or  a  westerly  motion,  since  the  rate  of  polar  motion  on 
any  given  parallel,  mass  multiplied  into  velocity,  in  the  upper 
strata  in  which  the  'air  moves  from  the  equator  toward  the 
poles,  is,  on  account  of  the  condition  of  continuity,  exactly 
equal  to  that  of  equatorial  motion  in  the  lower  strata,  in  which 
the  air  moves  from  the  poles  toward  the  equator;  and  so  the 
whole  force  deflecting  eastward  above,  arising  from  the  earth's 
rotation,  is  exactly  equal  to  that  deflecting  westward  below, 
and  these  being  in  contrary  directions,  there  is  no  force  arising 
directly  from  the  interchanging  motions  and  deflecting  forces 
to  overcome  the  friction  between  the  atmosphere  and  the 
earth's  surface.  This  force  arises  from  the  vertical  motions,  as 
explained  further  on  in  §  77.  But  whatever  east  or  west  com- 
ponents of  velocity  may  exist  at  the  earth's  surface,  there  are 
the  same  relative  velocities  of  these  components  all  the  way 
up  above,  so  that  all  the  absolute  east  or  west  components 
above  are  increased  algebraically  by  the  amount  of  velocity  at 
the  surface. 

75.  The  greater  the  absolute  east  components  of  velocity, 
the  greater  also  are  the  relative  velocities  and  the  friction 
between  the  strata,  so  that  for  a  given  amount  of  interchanging 
motion  between  the  equatorial  and  polar  regions  there  is  a 


CIRCULATION    WITH  EARTH  ROTATING   ON  ITS  AXIS.   IO9' 

limit  beyond  which  these  absolute  east  components  of  velocity 
cannot  go,  and  this  limit  is  where  the  frictional  resistance 
between  the  strata  becomes  equal  to  the  forces  which  overcome 
it  and  maintain  the  motions.  But  now  with  the  establishment 
of  these  east  components  of  motion,  increasing  with  increase 
of  altitude,  there  is  called  into  play  another  [deflecting  force 
depending  upon  the  earth's  rotation,  which  interferes  with  and 
diminishes  the  amount  of  interchanging  motion  between  the 
equatorial  and  the  polar  regions  which  would  exist  if  the  earth 
had  no  rotation  on  its  axis.  For  as  in  the  case  of  a  current  of 
air  flowing  from  the  equator  toward  the  pole  in  the  northern 
hemisphere  there  is  a  force  deflecting  to  the  right  or  east,  so  in. 
the  case  of  the  east  component  of  motion  there  is  also  a  force 
deflecting  toward  the  right  or  the  equator.  In  the  southern 
hemisphere  it  is  to  the  left,  but  still  toward  the  equator.  This 
force  is  contrary  to,  and  counteracts,  that  arising,  as  explained 
in  §  71,  from  the  temperature  gradient  between  the  equator 
and  the  pole.  The  greater  the  east  components  of  velocity  in 
the  atmosphere  above,  the  greater  this  force  ;  so  that  if  certain 
velocities  were  reached,  this  force  would  be  exactly  equal  to 
that  depending  upon  the  temperature  gradient,  and  the  inter- 
changing motion  between  the  equator  and  the  poles  could  not 
then  be  maintained,  and  without  some  motion  of  this  sort 
there  would  be  no  forces  to  overcome  the  friction  and  main- 
tain the  east  components  of  motion.  The  limit,  therefore, 
beyond  which  the  east  components  of  velocity  cannot  go  must 
fall  a  little  short  of  those  velocities  which  would  entirely  de- 
stroy the  force  which  keeps  up  the  interchanging  motions ;  but 
the  less  the  frictional  resistance  to  the  motions  the  more 
nearly  they  can  approach  to  this  limit,  and  in  the  case  of  no 
friction  the  east  components  of  velocity  which  would  satisfy  all 
the  conditions  of  the  problem  would  be  those  coming  up  to  the 
limit ;  for  in  this  case,  the  interchanging  motions  being  once 
established,  there  would  be  no  need  of  any  force  to  overcome 
friction  and  to  maintain  them. 

The  general  motions  of  the  atmosphere  and  their  relations- 
to  the  forces  producing  them,  in  the  case  of  an  earth  with  ro- 


110   THE   GENERAL    CIRCULATION  OF    THE  ATMOSPHERE. 

tation  on  its  axis,  are  similar  to  those  of  machinery  run  by  a 
steam-engine,  and  controlled  by  a  governor.  Without  this  the 
whole  force  would  be  applied  to  overcome  the  friction  and 
doing  the  work,  and  great  speed  might  be  obtained,  but  with 
the  governor  suitably  adjusted  there  is  a  certain  limit  beyond 
which  the  speed  cannot  go,  however  much  the  friction  or  work 
of  any  kind  may  be  diminished  ;  for  when  this  is  reached  all  the 
force  is  cut  off.  As  long,  therefore,  as  there  is  any  friction  to 
be  overcome  or  work  of  any  kind  to  be  done,  the  speed  must 
fall  a  little  short  of  this  limit,  and  it  can  only  reach  this  limit 
when  these  vanish.  So,  in  the  general  motions  of  the  atmos- 
phere in  case  of  no  rotation  of  the  earth  on  its  axis,  we  have 
.seen,  §  73,  the  whole  force  of  the  temperature  gradient  is 
brought  to  bear  in  overcoming  the  friction  and  maintaining  the 
interchanging  motion  between  the  equatorial  and  polar  regions, 
and  so  this  might  become  very  great.  But  in  the  case  of  the 
•earth  with  rotation  on  its  axis,  there  are  soon  developed  east 
•components  of  motion,  which,  by  means  of  the  consequent 
deflecting  forces,  in  a  great  measure  counteract  or  cut  off  the 
forces  which  give  rise  to  and  maintain  the  interchanging 
motion,  so  that  there  is  a  limit  beyond  which  the  speed  of  this 
motion  cannot  go  ;  for  if  this  limit  were  reached,  the  motions 
would  give  rise  to  east  components  of  motion  and  deflecting 
forces  which  would  entirely  counteract  the  forces  arising  from 
the  temperature  gradients. 

76.  The  limit  beyond  which  the  east  components  of 
velocity  cannot  go  may  be  determined  by  equating  the  ex- 
pression of  the  horizontal  force  for  unit  of  mass,  ge,  §  62,  with 
that  of  Fv ,  §  49,  which  is  the  deflecting  force  acting  in  the  direc- 
tion from  the  poles  toward  the  equator,  depending  upon  the 
east  components  of  velocity  v.  We  thus  get 

ge  •=.  (2n  -\-  r)v  sin  /. 

By  neglecting  v  in  comparison  with  2«,  as  we  may  without 
any  sensible  error  in  the  case  of  any  real  easterly  motions 
in  the  general  circulation  of  the  atmosphere,  we  get  from  the 
preceding  equation 


-CIRCULATION    WITH  EARTH  ROTATING   ON  ITS  AXIS.   Ill 


The  same  is  deducible  from  the  expression  of  e,  §  56,  by  chang- 
ing s  to  Vj  since  this  is  simply  the  special  case  in  the  general 
•expression  in  which  s  becomes  v.  This  limiting  value  of  v  can 
be  expressed  in  a  function  of  the  temperature  gradient  AT, 
instead  of  that  of  e,  the  gradient  of  the  isobaric  surface,  by 
putting  for  e  above  its  value  in  §  71.  We  thus  get 

ghAt 
= 


X  2»  sin  / 

using  for^-  and  2n  their  numerical  values  found  in  §  45,  in  ob- 
taining the  last  form  of  expression. 

Strictly,  the  value  of  h  in  this  expression  is  the  height  of  the 
isobaric  surface  if  the  atmosphere  had  the  temperature  of  o°  C.  ; 
but  as  the  average  temperature  up  to  a  considerable  altitude, 
and  for  all  latitudes,  does  not  differ  much  from  this  tempera- 
ture, this  value  of  h  in  any  case  differs  but  little  from  the  actual 
height  of  this  surface,  and  so  the  latter  may  be  used  for  ap- 
proximate results  without  much  error. 

If  AT  be  assumed  to  be  the  change  of  temperature  in  one 
•degree  of  latitude,  instead  of  one  meter,  then  we  must  divide 
this  expression  by  1  1  1,1  1  1,  the  number  of  meters  in  a  degree,  in 
order  to  obtain  the  expression  of  v  in  terms  of  the  temperature 
gradient  thus  expressed.  We  thus  get 

hAT 

V  —  0.00221  -  . 

sm  / 

Since  sin  /  becomes  small  towards,  and  vanishes  at,  the 
equator,  and  AT  is  supposed  to  do  the  same,  the  value  of  v  be- 
•comes  indeterminate  at,  and  very  uncertain  near,  the  equator, 
since,  where  sin  /  is  very  small,  a  small  inaccuracy  in  AT*  would 
give  rise  to  a  large  error  in  v* 

*  If  the  temperature  r  for  each  isobaric  surface  is  a  function  of  the  latitude 
of  the  form  A0-\-  A\  cos  2/,  in  which  A0  is  the  temperature  on  the  parallel  of 
45°  where  cos2/=o,  and  A\  is  the  half  difference  of  the  temperatures  at  the 


112   THE   GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

77.  So  far  we  have  considered  only  the  horizontal  motions, 
and  their  deflecting  forces  in  the  vertical  circulation  arising 
from  difference  of  temperature  between  the  equator  and  the 
poles,  and  have  obtained  the  preceding  results. 

We  come  now  to  consider  the  vertical  motions,  or  com- 
ponents of  motion,  downward  from  the  upper  strata  toward 
the  earth's  surface  in  the  higher  latitudes,  and  the  reverse  in 
the  lower  latitudes.  As  the  air  in  the  upper  strata  of  the 
higher  latitudes  with  its  large  east  component  of  velocity 
above  settles  down  toward  the  earth's  surface  where  this  com- 
ponent is  less,  it  gradually  loses  its  momentum,  and  the  effect 
of  this  lost  momentum  transferred  by  means  of  friction  from 
one  stratum  to  another  until  it  reaches  the  earth's  surface,  is 
spent  in  overcoming  the  friction  between  the  lower  stratum  and 
the  earth's  surface  and  maintaining  a  small  east  component  of 
velocity  of  the  air  at  and  near  the  surface. 

In  the  passage  of  the  air  of  the  upper  strata  from  the  equa- 
torial toward  the  polar  regions,  a  part  of  the  force  deflecting 
eastward  is  spent  in  overcoming  the  frictional  resistance  between 
the  strata  with  east  components  of  velocity  increasing  with 
increase  of  altitude,  which,  we  have  seen,  is  necessary  to  satisfy 
the  conditions,  and  the  other  part  is  spent  in  accumulating  the 
momentum  of  the  east  components  of  motion.  In  passing  in 

equator  and  the  pole,  then,  by  taking  the  differential  of  this  expression  and  sub- 
stituting the  small  variations  of  temperature  and  of  latitude  AT  and  Al,  respec- 
tively, for  the  corresponding  differentials  dr  and  dl,  we  have,  since  ^//has  been 
assumed  to  be  equal  to  unity  or  one  meter, 

AT  =  2,Al  sin  2^=4^1  sin  /cos  /. 

Substituting  this  expression  of  AT  in  the  first  of  the  preceding  expressions  of 

vt  we  get 

v  —  985.6/^1  cos  /. 

Since  v  here  is  proportional  to  cos  /,  and  this  to  the  distance  of  the  air  with 
velocity  v  from  the  axis  of  rotation,  the  velocities  which,  at  any  given  altitude 
h,  correspond  to  the  limit  of  velocities  which  can  be  reached,  are  those  which 
have  the  same  angular  velocity  with  reference  to  the  earth's  axis. 

The  values  of  A\  corresponding  to  the  mean  of  the  year,  and  January  and 
July  respectively,  according  to  the  table  of  §  68,  are  approximately  22°,  30°,  and 
14°,  as  deduced  from  the  northern  hemisphere.  The  temperature  gradient, 
therefore,  is  more  than  twice  as  great  in  January  as  in  July. 


CIRCULATION    WITH  EARTH  ROTATING   ON  ITS  AXIS.   113 

the  lower  strata  from  the  polar  toward  the  equatorial  regions, 
the  reverse  is  the  case,  and  part  of  the  force  now  tending  to 
deflect  westward  is  spent  in  overcoming  the  frictional  resistances 
to  a  west  component  of  motion,  whether  arising  from  the  strata 
above  having  greater  east  components  of  velocity,  or  from  the 
earth's  surface  below,  where,  in  the  lower  latitudes,  there  is  a 
west  component  of  motion,  and  the  balance  is  spent  in  over- 
coming the  momentum  of  the  east  component  of  motion  in  the 
higher  latitudes  already  acquired,  or  in  giving  rise  in  the  lower 
latitudes  to  the  momentum  of  the  west  components  of  motion. 
In  the  higher  latitudes,  therefore,  where  there  is  an  east  com- 
ponent of  motion  at  the  earth's  surface,  the  amount  of  east 
momentum  lost  by  any  portion  of  air  in  its  passage  above  from 
any  given  latitude  toward  the  pole  until  it  returns  below  to  the 
same  parallel,  is  the  kinetic  energy  which  it  has  contributed 
toward  overcoming  the  frictional  resistance  of  the  earth's  surface 
to  the  east  component  of  motion  at  the  surface  between  that 
parallel  and  the  pole ;  and  in  the  lower  latitudes,  where  there 
is  a  west  component  of  motion  at  the  earth's  surface,  the 
amount  of  west  momentum  lost  or  east  momentum  gained,  or, 
considered  algebraically,  the  amount  of  west  momentum  lost, 
by  any  portion  of  air  from  the  time  it  leaves  any  given  parallel 
of  latitude  in  its  passage  toward  the  equator  below  until  it 
returns  to  the  same  parallel  above,  is  the  amount  of  kinetic 
energy  which  it  has  contributed  towards  overcoming  the  fric- 
tional resistance  of  the  earth's  surface  to  the  west  components 
of  motion  between  that  parallel  and  the  equator. 

From  the  consideration,  therefore,  of  the  interchanging 
horizontal  and  vertical  motions  and  the  change  of  east  and 
west  momentum  as  the  vertical  motions  take  place,  we  see  there 
is  a  sort  of  torsional  force  arising  from  the  effect  of  the  earth's 
rotation  on  the  interchanging  motions  arising  from  the  tem- 
perature gradient,  which  tends  to  give  rise  to  and  maintain  an 
east  component  of  motion  of  the  atmosphere  at  the  earth's 
surface  in  the  higher  latitudes,  and  the  reverse  in  the  lower 
latitudes.  There  are,  however,  the  same  relative  velocities 
between  the  successive  strata,  since  the  forces  remain  the 


114  THE   GENERAL    CIRCULATION  OF   THE   ATMOSPHERE. 

same  which  overcome  the  friction  and  keep  up  these  relative 
velocities,  as  if  there  were  no  such  torsional  force,  or  the  fric- 
tional  resistance  to  east  or  west  components  of  motion  at  the 
earth's  surface  were  infinitely  great.  Whatever  velocities, 
therefore,  of  this  sort  are  given  to  the  lower  stratum  of  the 
atmosphere,  the  same  increase  of  velocity  is  also  given  to  all 
the  strata  up  to  the  top  of  the  atmosphere.  If  we  therefore 
put  v0  for  the  value  of  v  at  the  earth's  surface,  instead  of  the 
expression  of  ^0  in  §  76,  we  now  get 

Mr 

V  =  ^o  +  246.4- 


sin  /' 

in  which  AT:  is  the  change  of  temperature  in  the  distance  of 
one  meter.  If  At  expresses  the  change  in  the  distance  of  one 
degree  of  latitude,  then  0.00221  must  be  used  instead  of  the 
numerical  coefficient  246.4. 

According  to  this  expression  of  v,  the  east  components  of 
velocity  in  the  higher  latitudes  where  v0  is  positive  increase 
from  the  earth's  surface  to  the  top  of  the  atmosphere.  In  the 
lower  latitudes  where  v0  is  negative  or  a  west  component  the 
west  components  of  velocity  above  the  earth's  surface  decrease 
up  to  a  certain  altitude,  where  they  vanish  and  change  to  east 
components,  and  then  these  increase  to  the  top  of  the  atmos- 
phere. It  is  evident  that  the  higher  the  stratum  the  nearer  to 
the  equator  must  be  the  parallel  of  latitude  where  the  change 
from  west  to  east  components  of  motion  takes  place  until  that 
altitude  is  reached  where  there  is  no  west  component  of 
motion  at  any  parallel. 

78.  It  is  seen  from  this  expression  that  the  differences 
between  the  limiting  east  components  of  velocity  at  different 
altitudes,  and  approximately,  at  least  in  the  higher  latitudes, 
between  the  real  velocities,  are  proportional  to  AT,  and  so  to 
the  difference  of  temperature  between  the  equator  and  the 
poles.  But  the  amount  of  east  or  positive  momentum  lost  in 
a  given  time  while  the  air  in  the  higher  latitudes  is  descending 
from  higher  to  lower  altitudes,  and  west  or  negative  momen- 
tum, in  ascending  in  the  lower  latitudes  from  lower  to  higher 


CIRCULATION  WITH  EARTH  ROTATING   ON  ITS  AXIS.    115 

altitudes,  depend  both  upon  the  rate  of  change  in  the  east 
components  of  velocity  with  regard  to  change  of  altitude  and 
also  upon  the  speed  of  the  vertical  circulation.  This  latter,  if 
we  suppose  the  friction  between  the  strata,  moving  with  rela- 
tive velocities,  to  be  as  these  velocities,  is,  as  likewise  the 
former,  proportional  to  AT,  the  temperature  gradient  which 
.gives  rise  to  the  forces  overcoming  the  friction  and  maintaining 
the  circulation.  The  amount  of  east  or  west  momentum  lost 
in  a  given  time,  and  spent  in  overcoming  friction  between  the 
atmosphere  and  the  earth's  surface  and  giving  value  to  v9  is, 
therefore,  as  the  .square  of  AT,  or  as  the  square  of  the  differ- 
ence of  temperature  between  the  equator  and  the  poles.  If, 
then,  frictional  and  other  resistance  between  the  atmosphere 
and  the  earth's  surface  were  as  the  velocity,  the  value  of  v9 
would  have  to  be  as  the  square  of  AT,  and  so  about  four  times 
greater  in  winter  than  in  summer.  But  it  is  probable  that  the 
resistances  at  the  earth's  surface  increase  in  a  ratio  which  is 
greater  than  the  first  power  of  the  velocity,  and  if  so  the  value 
of  vt  would  have  to  increase  in  a  ratio  which  is  less  than  that 
of  the  square  of  At.  But  whatever  may  be  the  relation 
between  the  frictional  and  other  resistances  and  velocity,  the 
•values  of  v9  must  be  greater  in  winter  than  in  summer. 

The  relative  east  velocities  between  the  motions  of  the 
upper  strata  and  the  earth's  surface  are  likewise  greater  in 
winter  than  in  summer,  on  account  of  the  value  of  At  in  the 
expression  of  v  in  §  77  being  greater,  and  in  the  northern 
hemisphere  more  than  twice  greater  in  January  than  in  July. 
There  is,  then,  an  annual  inequality  in  the  east  and  west  com- 
ponents of  motion  of  the  atmosphere,  both  at  the  earth's 
surface  and  all  altitudes  above  the  surface,  such  that  the  east 
components  of  velocity  above  are  greater  in  January  than  in 
July,  and  in  the  middle  latitudes  of  the  northern  hemisphere, 
more  than  twice  as  great,  since  the  easterly  velocities  there  at 
the  earth's  surface  are  very  small. 

In  the  case  of  a  stratum  of  air  between  two  parallel  and 
vertical  plates  extending  from  the  equator  to  the  poles  and 
reaching  to  the  top  of  the  atmosphere,  the  horizontal  inter- 


Il6  THE   GENERAL    CIRCULATION  OF    THE  ATMOSPHERE. 

changing  motion  between  the  equatorial  and  polar  part  of  it. 
arising  from  a  vertical  circulation  would  not  give  rise  to  any 
force  which  would  tend  to  turn  the  polar  end  toward  the  east 
and  the  equatorial  toward  the  west,  if  it  were  free  to  turn 
around  some  vertical  axis  in  its  middle.  For  in  this  case  there 
would  be  no  east  momentum  lost  in  the  descent  of  the  air  in 
the  polar  end,  or  west  momentum,  in  its  ascent  at  the  equato- 
rial end,  and  the  deflecting  force  of  the  current  of  air  moving 
toward  the  pole  above,  and  causing  pressure  against  the  east 
side,  at  any  latitude,  would  be  exactly  counteracted  by  that  of 
an  equal  amount  of  motion  toward  the  equator  below,  and  caus- 
ing pressure  against  the  west  side.  In  this  case  no  part  of  the 
deflecting  forces  is  spent  in  creating  east  momentum  in  lower 
latitudes  which  is  lost  in  higher  latitudes,  and  vice  versa,  but  it 
is  all  spent  in  giving  rise  to  lateral  pressure. 

79.  There  is  still  another  effect  in  addition  to  the  preced- 
ing, though  much  smaller,  depending  upon  the  ascending  and 
descending  components  of  motion  in  the  vertical  circulation, 
which  tends  to  give  rise  to  and  maintain  an  east  component  of 
motion  in  the  higher  latitudes,  and  the  contrary  in  the  lower 
ones.  This  is  a  necessary  consequence  of  the  principle  of  the 
preservation  of  areas  in  the  case  of  central  and  centrifugal 
forces.  As  the  air  in  the  higher  latitudes  descends  toward  the 
earth's  surface  it  comes  nearer  to  the  earth's  axis ;  and  so,  if  free, 
must  have  a  proportionally  greater  absolute  gyratory  velocity 
around  this  axis,  and  consequently  a  greater  relative  velocity 
with  reference  to  the  earth's  surface. 

If  not  entirely  free,  this  tendency  to  acquire  an  increased 
east  component  of  velocity  causes  pressure  in  that  direction, 
which  tends  to  overcome  the  resistances  to  motion,  whether 
frictional  or  otherwise,  and  through  friction  between  the  differ- 
ent strata  is  communicated  to  the  earth's  surface.  In  the  lower 
latitudes  where  the  air  ascends  the  effect  is  the  reverse,  and 
tends  to  overcome  frictional  resistances  to  motions  from  east 
to  west,  and  is  likewise  communicated  through  friction  to  the 
earth's  surface.  In  the  preceding  case  of  a  vertical  stratum  of 
air,  free  to  turn  around  a  vertical  axis,  these  forces  being  in  art 


CIRCULATION    WITH  EARTH  ROTATING   ON  ITS  AXIS.    1 1/ 

east  direction  in  the  higher  latitudes  where  the  air  descends, 
and  the  contrary  in  the  lower  latitudes  where  it  ascends,  would 
both  tend  to  turn  the  vertical  stratum  horizontally  around  the 
vertical  axis.  The  formula  for  computing  the  absolute  gyra- 
tory velocity  of  a  projectile  or  any  free  body,  forced  directly 
upward,  and  consequently  the  loss  of  absolute  velocity,  and  the 
relative  west  velocity  acquired  at  any  given  altitude,  is  given 
in  §  60.  By  reversing  this  formula,  the  amount  of  relative  east 
velocity  acquired  in  falling  through  a  given  space,  if  the  body 
is  entirely  free,  can  be  likewise  computed.  On  account,  how- 
ever, of  the  small  depth  in  comparison  with  the  earth's  radius 
of  that  part  of  the  atmosphere  having  any  considerable  density, 
these  effects  are  very  small  for  the  atmosphere  generally. 

80.  The  relation  between  the  amount  of  the  east  compo- 
nents of  velocity  of  the  air  at  the  earth's  surface  in  the  higher 
latitudes,  and  that  of  the  west  components  in  the  lower  lati- 
tudes, is  determined  by  the  condition  that  the  sum  of  all  the 
forces  of  the  air-particles  of  the  higher  latitudes  acting  in  an 
•easterly  direction  upon  the  earth's  surface  through  friction  or 
resistance  of  any  kind,  multiplied  into  their  distances  from  the 
axis  of  rotation,  called  moments  of  couple,  must  be  exactly 
equal  to  similar  products  in  the  lower  latitudes,  where  there  is 
a  west  component  of  motion,  and  the  forces  by  means  of  fric- 
tional  and  other  resistances  act  in  the  contrary  direction.  If 
this  condition  were  not  satisfied  there  would  be  a  residual  un- 
counteracted  force  acting  in  the  one  direction  or  the  other 
tending  to  change  the  velocity  of  rotation ;  but  this  can  only 
arise  from  external  forces  which  do  not  act  in  the  direction  of 
the  axis  of  rotation,  and  not  from  any  central  forces,  or  such 
as  act  only  in  the  planes  of  the  meridians,  and  which  conse- 
quently have  no  gyratory  components  of  force,  for  the  actions 
and  reactions  in  the  motions  arising  from  such  forces,  being 
•exactly  equal  and  in  contrary  directions,  where  the  mass  as  a 
whole  remains  at  the  same  distance  from  the  centre,  cannot 
affect  the  velocity  of  rotation.  This  principle  was  recognized 
by  Hadley  in  his  theory  of  the  trade-winds,  for  he  states  that 
•"all  motions  in  any  direction  must  have  their  counter-motions, 


Il8    THE    GENERAL    CIRCULATION  OF   THE  ATMOSPHERE.. 

else  the  effect  upon  the  earth's  surface  would  be  to  change  the 
earth's  rotation  upon  its  axis." 

The  forces  exerted  upon  the  earth's  surface  tending  to  turn 
the  earth  on  its  axis  are  effective  in  proportion  to  the  distance 
from  the  axis  at  which  these  forces  are  applied.  This  is  not 
only  in  accordance  with  a  well-established  principle  in  mechan- 
ics, but  also  with  almost  every  one's  experience.  One  man  at 
the  end  of  a  lever  of  a  given  length  can  turn  a  capstan  which 
would  require  two  men  of  equal  strength  with  levers  of  only 
half  the  length.  The  forces,  therefore,  have  to  be  multiplied 
into  the  distances  from  the  axis,  and  then  the  forces  of  equal 
products  have  equal  tendencies  to  turn  the  earth  on  its  axis^ 
If  a  given  gyratory  force  were  applied  on  the  parallel  of  6o°r 
where  the  distance  from  the  axis  is  only  half  as  great  as  at  the 
equator,  its  effectiveness  in  turning  the  earth  on  its  axis  would 
be  counteracted  by  half  the  amount  of  this  force  applied  in 
the  contrary  way  at  the  equator,  and  it  would  require  twice  as 
much  of  the  former  to  counteract  the  latter.  The  east  com- 
ponents of  velocity,  therefore,  in  the  higher  latitudes,  where 
the  distances  from  the  axis  are  much  less,  must  be  much  great- 
er than  the  west  components  in  the  lower  latitudes  where,  the 
distances  from  the  axis  are  much  greater,  if  we  suppose  the 
surface  of  the  earth  to  be  homogeneous,  so  that  equal  veloci- 
ties meet  with  equal  resistances  and  so  exert  equal  forces  upon- 
the  earth's  surface,  or  else  the  east  components  of  velocity 
must  comprise  a  much  greater  amount  of  air.  The  quantity 
of  air  is  equally  divided  by  the  parallel  of  30°,  and  therefore 
the  east  components  of  the  higher  latitudes  at  the  earth's  sur- 
face must  be  much  greater  than  the  west  components  in  the 
lower  latitudes,  or  else  the  dividing  parallel  between  the  east 
and  west  components  of  motion  at  the  earth's  surface  must  be 
nearer  the  equator,  on  the  average,  than  the  parallel  of  30°. 

81.  The  velocities  of  the  east  and  west  components  at  the 
earth's  surface  depending  upon  the  forces  of  momentum,  as 
explained  in  §  77,  depend  very  much  upon  the  nature  of  that 
surface.  For  the  velocities  increase  until  the  resistances  to 
the  motions  are  equal  to  the  forces  producing  them,  so  that 


CIRCULATION    WITH  EARTH  ROTATING   ON  ITS   AXIS.   119 

the  smoother  the  surface,  and  the  less  the  friction  between  the 
air  and  that  surface,  the  greater  the  velocities.  If  there  were 
no  resistances  from  the  earth's  surface  these  velocities  would 
be  very  great — somewhat  as  given  in  §  48,  but  on  account  of  the 
smallness  of  the  forces  giving  rise  to  them,  and  maintaining 
them  by  overcoming  the  friction  when  they  are  once  estab- 
lished, these  velocities  are  comparatively  very  small.  Since 
they  depend  upon  the  amount  of  resistance  to  the  motion, 
they  must,  in  general,  be  greater  on  land  than  on  the  ocean  on 
the  same  latitudes,  and  since  there  is  little  land  in  the  southern 
hemisphere  in  comparison  with  that  of  the  northern,  they  must 
be  much  greater  in  the  former  than  in  the  latter.  The  values 
of  v0 ,  therefore,  in  the  expression  of  the  limiting  value  of  v,  § 
77,  are  much  greater  on  the  several  parallels  of  latitude  of  the 
southern  hemisphere  than  on  corresponding  parallels  of  the 
northern  hemisphere,  especially  for  the  higher  latitudes,  where, 
in  the  southern  hemisphere,  the  ocean  extends  entirely  around 
the  globe.  The  east  components  of  velocity,  therefore,  at  all 
altitudes  in  the  higher  latitudes,  where  v0  is  positive,  or  at  least 
the  limits  of  these  velocities,  must  be  greater  in  the  southern 
than  in  the  northern  hemisphere  by  the  same  amount  that  z>0 
is,  since  the  relations  between  the  east  components  of  velocity 
of  the  strata  above  the  earth's  surface  remain  the  same  what- 
ever those  velocities  may  be  at  the  surface. 

The  whole  system  of  atmospheric  circulation  is  so  complex 
and  the  friction  constant  of  the  atmosphere  and  the  resistances 
from  the  earth's  surface  so  uncertain,  that  it  is  impossible  to 
compute  the  values  of  v0  from  the  known  forces ;  and  all  that 
can  be  obtained  from  theory  is  an  indication  that  there  must 
be  motions  in  certain  directions,  and  that  these  must  be  greater 
or  less  according  to  the  variations  of  the  forces  at  different 
times  and  the  resistances  of  the  earth's  surface  at  different 
places.  Even  the  values  of  VQ  are  very  imperfectly  known 
from  direct  observation,  though  this  indicates  that  there  are 
such  values,  positive  in  the  higher  and  negative  in  the  lower 
latitudes. 

82.  We  have  seen  that  in  the  case  of  no  frictional  resist- 


120   THE   GENERAL    CIRCULATION  OF    THE   ATMOSPHERE. 

ances  to  the  motions  of  the  atmosphere  the  east  components 
of  velocity  of  the  different  strata  on  any  given  parallel  of  lati- 
tude come  up  to  the  limit  as  given  by  the  expression  of  v 
in  §  77,  whatever  the  surface  value  VQ  may  be,  and  that  in  this 
c.ase  there  is  no  necessity  for  any  meridional  interchanging 
motion  to  overcome  the  friction  of  these  east  components  of 
motion.  In  the  case  of  friction,  therefore,  the  less  the  friction, 
and  the  greater  the  deflecting  force  belonging  to  a  given 
amount  of  meridional  motion,  the  less  of  this  motion  is  re- 
quited to  overcome  the  friction  of  the  east  component  of  mo- 
tion. The  frictional  resistance  to  the  motions  of  the  atmos- 
phere, except  near  the  earth's  surface,  are  so  small  that  a  very 
little  interchanging  motion  between  the  equatorial  and  polar 
regions  is  required  to  give  force  enough  to  overcome  the  re- 
sistance to  the  east  component  of  motion,  especially  in  the 
higher  latitudes  where  sin  /  in  the  expression  of  this  force,  § 
49,  is  large.  In  the  higher  altitudes,  therefore,  where  the  east 
components  of  velocity  are  great  in  comparison  with  the  velocity 
of  the  interchanging  motion,  the  resultant  direction  must  be  very 
nearly  from  west  to  east,  being  a  little  north  of  east  in  high 
altitudes  where  the  interchanging  motion  is  toward  the  pole, 
and  a  little  south  of  east  in  the  lower  strata  where  it  is  from 
the  pole. 

In  the  lower  latitudes,  however,  where  the  deflecting  forces 
depending  upon  the  earth's  rotation  are  small  in  consequence  of 
the  smallness  of  sin  /,  the  relative  velocities  between  the  strata, 
and  the  absolute  east  components  of  velocity  in  the  strata  above, 
are  less  than  in  higher  latitudes  for  the  same  interchanging 
velocity,  and  so  the  resultant  motion  deviates  more  from  an  east 
direction.  The  motions  here,  both  in  velocity  and  direction, 
become  more  nearly  such  as  they  would  be  in  the  case  of  an 
earth  without  rotation,  in  which  case  they  would  be  in  the 
planes  of  the  meridians  and  would  become  comparatively  very 
rapid.  At  the  altitudes  in  these  latitudes  where  the  west  com- 
ponent of  motion  changes  to  an  east  component  there  is  very 
little  motion  in  any  direction,  and  so  the  direction  is  very  un- 
certain ;  but  at  still  lower  altitudes,  where  there  is  a  west  com- 


COMPARISONS    WITH  OBSERVATIONS.  121 

^ponent  of  motion,  this  combined  with  the  component  of  motion 
toward  the  equator  gives  rise  to  the  trade-winds  in  the  lower 
strata  of  these  latitudes. 

At  the  equator  the  deflecting  forces  giving  rise  to  east 
motions  entirely  vanish,  and  hence  here  there  are  no  such 
motions ;  and  as  the  horizontal  interchanging  motions  also 
vanish  here,  or  at  least  at  the  thermal  equator,  on  account  of 
the  vanishing  of  the  temperature  gradient,  there  can  be  no 
such  motion  here.  Though  there  may  be  a  westerly  motion 
at  a  considerable  altitude  above  the  earth's  surface  arising 
from  the  unchecked  momentum  of  the  west  component  of  mo- 
tion acquired  as  the  air  moves  in  from  both  sides  toward  the 
equator. 

COMPARISONS   WITH   OBSERVATIONS. 

83.  The  preceding  theoretical  deductions,  so  far  made,, 
with  regard  to  the  general  circulation  of  the  atmosphere,  must 
be  understood  to  be  those  simply  which  depend  upon  the  nor- 
mal temperature  gradient  between  the  equator  and  the  poles, 
unaffected  by  abnormal  local  and  temporary  disturbances  of 
temperature.  Hence  in  these  comparisons  the  prevailing  mo- 
tions and  directions  of  the  air,  observed  at  different  times  and 
places,  and  not  individual  observations,  made  in  one  locality, 
must  be  used. 

With  regard  to  the  strong  easterly  currents  of  the  upper 
strata  of  the  atmosphere  in  nearly  all  latitudes,  as  deduced 
from  theoretical  considerations  in  the  preceding  pages,  any  one 
of  ordinary  observing  habits  could  scarcely  live  a  week  upon 
the  earth  without  discovering  from  the  motions  of  the  clouds, 
and  especially  the  very  high  cirrus  clouds,  that  the  general 
tendency  of  the  air  above  is  easterly,  even  in  the  lower  lati- 
tudes where,  in  the  lower  strata,  there  is  a  west  component  of 
motion,  and  that  the  velocities  above  in  the  middle  and  higher 
latitudes  are  much  greater  than  at  and  near  the  earth's  surface. 
Espy  says :  "  I  have  found  the  true  cirrus  clouds  to  average 
scarcely  once  a  year  from  any  eastern  direction;  and  when  they 


122    THE    GENERAL    CIRCULATION  OF   THE   ATMOSPHERE. 

do  come  from  that  direction,  it  is  only  when  there  is  a  storm' 
of  uncommon  violence  in  the  east."  Mr.  Ley  also,  in  his  nu- 
merous observations  of  the  cirrus  clouds,  almost  universally 
found  them  to  have  an  easterly  motion,  from  which  they  rarely 
deviated.  From  these  observations  it  is  evident  that  the  pre- 
vailing normal  currents  in  the  regions  of  these  clouds  is  easter- 
ly, and  with  a  velocity  so  great  that  abnormal  temporary  dis- 
turbances of  the  atmosphere  are  rarely  sufficient  to  reverse- 
their  directions. 

At  Toronto,  Canada,  the  resultant  directions  of  the  clouds,. 
as  ascertained  from  a  very  long  series  of  observations,  are  as- 

follows : 

\ 

Spring.  Summer.  Autumn.  Winter. 

N.  83°  W.         N.  75°  W.         N.  8i°W.         N.  78°  W. 

Here,  at  all  seasons  of  the  year,  the  resultant  directions  of 
cloud-motion  are  from  a  direction  a  little  north  of  west, 
indicating  that  the  principal  component  of  motion  is  an  east 
component  in  accordance  with  theory.  The  other  component,, 
being  a  southern  one,  indicates  that  the  clouds  observed  were 
mostly  down  in  the  lower  strata  of  the  atmosphere,  below  the 
neutral  plane,  where  the  interchanging  motion  is  from  the  pole. 
toward  the  equator. 

That  there  is  a  strong  easterly  current  prevailing  at  great 
altitudes  in  the  atmosphere,  deviating  but  little  from  an  east 
direction,  even  as  near  the  equator  as  the  parallel  of  30°, 
which  the  great  local  and  temporary  disturbances  to  which 
the  atmosphere  is  subject  scarcely  ever  reverses,  or  even 
changes  much  in  direction,  is  shown  from  the  results  of  four 
years'  observations  of  the  directions  of  the  cirrus  clouds  at 
Zi-ka-wei,11  latitude  31°  12'  N.,  longitude  121°  26'  E.  These- 
give,  for  the  four  years, 

Directions N.      N.N.E.       N.E.         E.N.E.         E.         E.S.E.         S.E.        S  S.E. 

Frequency 13  i  6  15021 

Directions S.      S.S.W.       S.W.       W.S.W.       W.      W.N.W.      N.W.      N.N.W.. 

Frequency 3  6  43  69  395  24  18  i 

Here  the  direction  of  by  far    the  greatest    frequency  is  the: 


COMPARISONS    WITH  OBSERVATIONS.  123- 

western  one,  comparatively  few  being  even  from  the  adjacent 
directions  given ;  and  as  there  are  a  few  more  motions  from 
W.S.W.  than  from  W.N.W.,  and  from  S.W.  than  from  N.W., 
they  indicate  that  the  normal  current  has  a  small  northern 
component.  The  results,  therefore,  are  strictly  in  accordance 
with  theory,  §  82,  which  requires  that  there  should  be  a 
motion  toward  the  pole  at  high  altitudes,  with  a  velocity^ 
small  in  comparison  with  that  of  the  east  component  of 
motion. 

Even  much  nearer  the  equator,  at  Colonia  Tover,  Vene- 
zuela, latitude  10°  26',  observations  of  the  directions  of  the 
clouds  indicate  that  the  principal  component  of  motion  above 
is  an  eastern  one,  while  in  the  lower  strata  the  motions  have 
a  west  component,  as  required  by  theory.  While  the  motions, 
of  the  upper  clouds  were  generally  from  some  westerly  point, 
those  of  the  lower  ones  were  from  some  easterly  direction.12 

84.  The  theoretical  deductions  of  the  preceding  pages  are 
also  confirmed  by  the  observations  of  the   directions  in  which, 
the  smoke  and   ashes  of  active  volcanoes  have  been   carried. 
On  the  first  of  May,   1812,  the  island   of  Barbadoes  was  sud- 
denly obscured  by  a  shower  of  ashes  from  an  eruptive  volcano- 
of  St.  Vincent,  West  Indies,  more  than  a  hundred  miles  to  the, 
westward.13     Although  the  motion  of  the  air  here  in  the  lower 
strata  has  a  western  component,  yet  the  ashes  were  carried  up 
to  altitudes  where  the  principal  component  of  motion  is  toward 
the  east,  and  hence  the  ashes  were  drifted  in  that  direction. 
Also  on  the  2Oth  of  January,  1835,  the  volcano  of  Coseguina, 
Central  America,  lying  in  the  belt  of  the  north-easterly  trade- 
winds,  sent  forth  great   quantities  of  lava  and   ashes,  and  the 
latter  were  borne  in  a   direction  just   contrary  to  that  of  the 
surface  winds,  and  lodged  on  the  island  of  Jamaica,  800  miles 
to   the   east-northeast.13     In    this   case,    also,    the   ashes   were 
carried  up   to  altitudes  where  the  prevailing  direction  of  the 
current  of  air  was  a  little  north  of  east,  the  northern  component 
arising  from  the  general  poleward    motion    of   the   air  at  all, 
latitudes  in  the  upper  strata  of  the  atmosphere. 

With   regard   to   the   volcanic   eruption   of   the   island  of! 


124   THE   GENERAL    CIRCULATION  OF    THE  ATMOSPHERE.  • 

Sumbawa,  about  200  miles  east   of  the  eastern  part  of  Java, 
Lyellsays:14 

"  On  the  side  of  Java  the  ashes  were  carried  to  the  distance  of  300, 
and  217  miles  toward  Celebes,  in  sufficient  quantities  to  darken  the  air. 
The  floating  cinders  to  the  westward  of  Sumatra  formed  on  the  I2th  of 
April  a  mass  two  feet  thick  and  several  miles  in  extent,  through  which 
ships  with  difficulty  forced  their  way. 

"  The  darkness  occasioned  in  day-time  by  the  ashes  in  Java  was  so 
profound,  that  nothing  equal  to  it  was  ever  witnessed  in  the  darkest 
night.  Although  the  volcanic  dust  when  it  fell  was  an  impalpable 
powder,  it  was  of  considerable  weight  when  compressed  :  a  pint  of  it 
weighed  twelve  ounces  and  three  quarters.  '  Some  of  the  finest  particles,' 
says  Mr.  Crawford,  '  were  transported  to  the  islands  of  Amboyna  and 
Banda,  which  last  is  about  800  miles  east  from  the  site  of  the  volcano, 
although  the  southeast  monsoon  was  then  at  its  height.'  They  must 
have  been  projected,  therefore,  into  the  upper  regions  of  the  atmosphere, 
where  a  counter  current  prevailed." 

Notwithstanding  this  volcano  was  only  a  few  degrees  from 
the  equator,  yet  it  seems  the  finer  ashes  were  carried  to  so  great 
a  distance  eastward  by  the  currents  above,  while  the  southeast 
trade-wind  below,  strengthened  by  the  southeast  monsoon  pre- 
vailing at  the  time,  carried  the  coarser  particles  in  nearly  the 
•contrary  direction. 

In  the  account  of  the  volcanic  eruptions  of  Krakatoa  of  the 
latter  part  of  May,  1883,  it  is  stated:15 

"  The  volcano  was  ejecting,  with  a  great  noise,  masses  of  pumice, 
molten  stone,  and  volumes  of  steam  and  smoke,  part  of  which  was 
carried  away  westward  by  the  monsoon  wind/dropping  all  around  and 
close  at  hand  its  larger  pieces,  while  a  high  rising  cloud  is  especially 
recorded  as  driving  away  eastward,  having  evidently  encountered  a  cur- 
rent in  that  direction  in  the  upper  air.  Some  of  this  dust-cloud  was 
carried  far  to  the  eastward,  for  Mr.  Forbes  relates  that  on  the  morning  of 
the  24th  of  May,  when  in  the  island  of  Timor,  twelve  hundred  miles 
distant,  he  observed  on  the  veranda  of  his  hut,  situated  high  in  the  hills 
behind  Dilly,  a  sprinkling  of  small  particles  of  grayish  cinder,  to  which 
his  attention  was  more  particularly  drawn  later  on,  and  the  next  day  by 
their  repeated  falling  on  the  page  before  him." 

Here  again,  only  a  few  degrees  south  of  the  equator,  we 


COMPARISONS    WITH  OBSERVATIONS.  12$, 

have  evidence  that  while  in  the  lower  strata  there  was  a  current 
which  carried  the  coarser  parts  of  the  ejecta  westward,  there 
was  a  strong  upper  current  which  carried  the  cloud  of  steam, 
smoke,  and  finer  ashes,  which  ascended  to  great  altitudes,  away 
to  the  east. 

85.  The  general  easterly  tendency  of  nearly  the  whole  upper 
part  of  the  atmosphere  is  not  only  shown  from  observed  cloud- 
motions  and  the  drift  of  the  smoke  and  ashes  of  volcanoes,  but 
also  from  observations  of  the  winds  on  all  high  peaks  and 
mountain  ranges.  Very  strong  and  prevailing  westerly  winds, 
have  been  observed  on  Mauna  Loa  in  the  Sandwich  Islands, 
on  the  tops  of  Pike's  Peak  and  of  Mount  Washington,  in  all 
the  passes  and  on  all  the  peaks  of  the  Rocky  Mountains  and  the 
Andes,  on  the  Peak  of  Teneriffe,  the  Himalayas  of  Asia,  and 
at  every  elevated  position  in  either  hemisphere  all  around  the 
globe,  except  at  and  near  the  equator,  even  in  the  trade-wind 
zones,  where,  at  the  same  time,  there  is  a  wind  of  considerable 
strength  from  nearly  the  opposite  direction.  Leopold  von 
Buch  says  with  regard  to  the  Peak  of  TenerifTe : 13  "  It  is  hard  to 
find  any  account  of  an  ascent  of  the  Peak  in  which  the  strong 
west  wind  which  has  been  met  with  on  the  summit  has  not  been 
mentioned.  Humboldt  ascended  the  Peak  on  the  2ist  of  June  ; 
when  he  reached  the  edge  of  the  crater  he  could  scarcely  keep 
his  feet,  such  was  the  violence  of  the  west  wind." 

The  following  are  the  relative  frequencies  of  the  winds  on 
Pike's  Peak  from  the  several  directions,  as  given  by  10  years  of 
observations  of  the  Signal  Service  1873-1883,  inclusive  :16 

Directions N.         N.E.         E.         S.E.         S.         S.W.         W.         N.W. 

Rel.  Frequencies. .  .8  13  2  2  4  36  17  18 

From  these  results  from  the  observations  of  direction  mere- 
ly, it  is  evident  that  at  the  top  of  the  Peak  the  current,  on  the 
average,  is  easterly,  with  a  considerable  polar  component.  The 
latter  is  indicated  by  the  relative  frequency  from  the  S.W.  be- 
ing twice  as  great  as  that  from  the  N.W.,  though  the  contrary  is. 
indicated  by  the  much  greater  relative  frequency  from  the  N.E.. 
than  from  the  S.E.,  but  this  should  have  much  less  weight.  We- 


-126   THE   GENERAL    CIRCULATION  OF    THE  ATMOSPHERE. 

cannot  infer,  however,  from  the  results  of  these  observations 
that  Pike's  Peak  reaches  up  to  where  the  general  motion  is  to- 
ward the  pole,  since  the  winds  of  this  locality  may  be  affected 
by  an  abnormal  local  disturbance  of  some  kind. 

For  the  top  of  Mt.  Washington,  from  three  years'  observa- 
tions, Loomis  found  the  resultant  direction  of  the  wind  N.  76° 
W.  This  and  the  resultants  from  cloud  observations  at  Toronto, 
§  83,  indicate  that  the  general  current  at  the  top  of  Mt.  Wash- 
ington, and  at  the  average  altitudes  of  the  clouds  generally,  has 
-a  south  component  of  motion  at  these  latitudes,  as  required 
£>y  theory. 

In  the  high  latitudes  of  Asia  it  also  appears  that  the  direc- 
tion of  the  wind  on  high  mountain  tops  is  easterly,  and  with  a 
south  component  of  motion.  "  At  Mt.  Alibut,  200  miles  west 
-of  Irkutsk,  and  over  7000  feet  high,  a  very  constant  and  strong 
W.N.W.  wind  is  observed."  20 

86.  While  theory  indicates  that  the  whole  upper  part  of 
the  atmosphere,  except  at  and  near  the  equator,  must  have  an 
easterly  motion  with  velocity  increasing  with  increase  of  alti- 
tude, and  the  existence  of  such  a  motion  is  confirmed  by  all 
-observations,  it  is  evident  from  the  Report  of  the  Krakatoa 
'Committee  of  the  Royal  Society  that  at  very  high  altitudes  at 
-and  near  the  equator  there  must  have  been,  in  the  latter  part 
of  August,  1883,  a  strong  current  from  east  to  west  of  at  least 
70  miles  per  hour,  by  which  the  dust-particles  causing  the  sun- 
set glows  and  other  phenomena  were  carried  in  this  direction 
around  the  globe.  According  to  the  observations,  also,  of  the. 
Hon.  Ralph  Abercromby  in  the  equatorial  regions  in  the  months 
>of  December  and  May,  there  is  likewise  a  westerly  current  here 
at  the  altitudes  of  the  cirrus  clouds,  though  only  a  few  degrees 
south  of  the  equator  there  seemed  to  be  an  east  component  of 
motion.  For  such  currents  theory  furnishes  a  slight  force,  § 
'60,  arising  from  the  ascent  of  air  in  the  equatorial  region,  which 
tends  to  give  rise  to  a  westerly  current,  which,  if  it  were  not 
for  friction,  would  be  considerable  at  great  altitudes.  This 
current,  it  is  seen,  if  the  motions  were  without  friction,  as  in 
the  case  of  a  projectile  in  a  vacuum,  would  have  a  velocity  of 


COMPARISONS    WITH  OBSERVATIONS.  I2/ 

•only  0.73  m.  per  second  at  the  altitude  of  10  kilometers,  and 
a  velocity  of  70  miles  per  hour  would  require,  by  the  formula, 
an  altitude  of  about  270  miles.  This  is  not,  therefore,  an  ade- 
quate cause  of  itself  for  the  existence  of  such  currents.  But 
in  addition  to  this  there  are  the  northeast  and  southeast  trade- 
•\vinds,  extending  up  to  a  considerable  altitude,  and  coming  in 
•obliquely  from  both  sides  toward  the  equator,  or  rather  the 
-doldrums  a  little  north  of  the  equator,  and  the  deflecting  force 
Tvhich  produces  the  western  component  of  velocity  is  counter- 
acted by  friction,  except  at  and  near  the  earth's  surface,  only 
after  considerable  westerly  velocity  is  acquired ;  for  friction 
can  only  be  brought  into  play  where  there  is  a  relative  velocity 
between  different  strata,  and  so  the  velocity  must  increase  with 
increase  of  altitude,  and  become  large  at  high  altitudes. 

But,  besides  the  preceding,  there  is  another  cause  for  westerly 
currents  at  high  altitudes  in  the  equatorial  regions  during  the 
summer  and  winter  seasons  of  the  year.  When  both  hemi- 
spheres have  about  the  same  temperature  there  is  little  or  no 
•interchange  of  air  between  them,  and  so,  little  or  no  current 
-crossing  the  equatorial  regions  in  either  direction,  either  above 
or  below.  But  at  other  times,  during  the  summer  of  the  north- 
ern hemisphere  for  instance,  there  is  a  current  from  the  northern 
to  the  southern  hemisphere  above,  and  the  reverse  below,  and 
it  is  readily  seen  that  the  current  above,  considered  by  itself 
•and  not  in  connection  with  the  interchanging  motions  between 
.  the  equatorial  and  polar  regions  at  a  mean  annual  temperature, 
in  approaching  the  equator  tends  to  acquire,  by  the  deflecting 
force  of  the  earth's  rotation,  a  western  component  of  motion, 
which  continues  to  increase  until  the  friction,  which  is  small 
here,  exactly  counteracts  this  tendency,  and  mostly  after  the 
air  passes  the  equator  and  the  deflecting  force  changes  to  the 
left  of  the  direction  of  motion,  is  this  western  component  grad- 
ually decreased  and  at  a  short  distance  south  of  the  equator 
•changed  to  an  eastern  component  of  motion,  though  the  effect 
of  friction  takes  place  in  some  measure  before  the  air  arrives 
-at  the  equator,  and  while  the  deflecting  force  to  the  right,  north 
of  the  equator,  is  vanishing.  As  the  friction  above  is  small, 


128   THE    GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

the  velocity  required  above  to  give  rise  to  friction  enough  to> 
counteract  the  deflecting  force,  and  to  overcome  the  momentum 
of  the  western  component  of  motion,  may  be  very  great. 

If  there  were  no  friction  between  the  air  and  the  earth's 
surface,  of  course  the  contrary  effect  would  be  produced  in  the 
lower  part  of  the  atmosphere  where  the  interchanging  motion 
is  from  south  to  north,  and  there  would  be,  then,  an  east  com- 
ponent of  motion.  But  the  great  amount  of  friction  at  the 
earth's  surface  prevents  such  a  result,  and  so  the  western  com- 
ponent above  is  increased  thereby,  for  the  relative  velocities 
between  the  different  strata  must  be  such  as  to  counteract  the 
deflecting  forces  in  the  one  direction  above  and  the  contrary 
below.  Of  course  similar  effects  in  the  same  directions,  and 
perhaps  of  the  same  magnitudes,  are  produced  at  the  opposite- 
season  of  the  year,  when  the  interchanging  currents  above  and 
below  are  reversed  in  direction. 

At  the  time  of  the  Krakatoa  eruption  the  latter  part  of 
August,  the  effect  arising  from  this  cause,  in  giving  rise  to  a 
westerly  current  at  high  altitudes,  would  be  near  its  maximum, 
and  it  is  probable  that  if  it  had  occurred  at  a  time  when  the 
two  hemispheres  had  nearly  the  same  temperature,  the  dust- 
particles  and  their  accompanying  phenomena  would  not  have 
been  transferred  westwardly  so  rapidly.  Observations,  also, 
upon  the  motions  of  the  cirrus  clouds  at  such  a  time  would  per- 
haps not  indicate  so  much  of  a  western  component  of  motion 
as  during  the  extremes  of  summer  and  winter. 

At  the  time  of  the  great  Krakatoa  eruptions  the  great  mon- 
soon influence,  no  doubt,  played  an  important  part ;  for  then 
the  doldrums  and  the  place  of  meeting  of  northerly  and  south- 
erly currents  were  transferred  to  the  north  of  India,  and  the 
great  return  current  above  toward  the  equator  was  powerfully 
deflected  toward  the  west,  while  the  contrary  took  place  below.. 
This  higher  current,  moving  toward  the  south  and  west,  carried 
the  higher  dust-particles  down  toward  Madagascar,  while  in 
the  lower  or  medium  strata  the  current  carried  them  toward 
Japan,  thus  causing  the  apparent  initial  streams  or  branches  in, 
these  directions. 


COMPARISONS    WITH  OBSERVATIONS.  12Q 

87.  We  have  seen,  §  77,  that,  according  to  theory,  the  at- 
mosphere at  the  earth's  surface  has  an  easterly  tendency  in  the 
higher  latitudes,  and  the  contrary  in  the  lower  ones.  It  must 
be  evident  to  almost  every  one  that  in  the  middle  and  higher 
latitudes  winds  with  a  principal  west  component  are  both  the 
strongest  and  most  frequent,  and  that  in  the  latitudes  of  the 
trade-winds  the  west  component,  especially  upon  the  great 
oceans,  is  well  marked,  and  without  much  variation.  The  few 
observations  which  we  have  from  the  interior  of  North  Africa 
indicate  that  the  prevailing  winds  are  easterly  and  northeasterly. 
This  is  also  shown  to  be  the  case  on  the  northwest  coast  of 
Africa  in  the  trade-wind  latitudes  by  the  sand  and  dust  which 
is  blown  out  into  the  Atlantic  Ocean  by  the  prevailing  winds 
there.  According  to  Mr.  Laughton,18  "  The  sand  which  these 
winds  raise  in  the  desert  is  carried  by  them  far  out  to  sea. 
During  the  summer  it  fills  the  air  as  far  as  the  Canaries  and  to- 
the  height  of  the  Peak  of  Teneriffe  with  an  impalpable  dust, 
which  has  the  effect  of  a  thick  haze  ;  and  at  all  seasons  of  the 
year  ships,  even  at  a  considerable  distance  from  the  shore,  find- 
it  covering  their  sails  and  decks." 

Professor  Piazzi  Smyth,  also,  observed  on  the  Peak  of 
Teneriffe  "  that  the  dust  haze,  which  almost  constantly  filled 
the  atmosphere  and  rendered  the  view  very  indistinct,  was  in 
the  stratum  of  air  moving  from  the  eastward,  that  high  over- 
head the  air  was  clear,  and  that  when  the  westerly  wind  de- 
scended to  their  level  all  traces  of  the  dust  haze  in  their  im- 
mediate neighborhood  vanished."  ]  Of  course  these  general 
tendencies  are  very  much  changed  frequently  by  the  numerous 
local  and  temporary  disturbances,  especially  upon  land,  so  that 
the  directions,  temporarily,  are  often  nearly  or  quite  reversed 
from  that  of  the  general  tendency. 

The  average  velocity  of  resultant  motion  of  the  air  at  the 
earth's  surface  for  the  whole  year  at  a  great  many  stations  in 
all  parts  of  the  United  States,  according  to  the  estimates  of 
Coffin,  is  about  two  miles  per  hour  with  a  resultant  direction  a 
little  north  of  east.  The  east  component  of  motion  is,  therefore, 
very  nearly  the  same.  These  estimates,  however,  are  extremely 


130   THE   GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

vague  and  uncertain,  being  based  mostly  upon  the  relative  fre- 
quency of  the  winds  from  the  different  principal  points  of  the 
compass.  Unfortunately  the  numerous  observations  of  the 
Signal  Service,  as  given  in  the  Reports  of  the  Chief  Signal 
Officer,  are  of  little  avail  in  determining  such  resultants,  since 
only  the  relative  frequencies  of  direction  from  the  different 
points  are  given,  and  not  the  corresponding  velocities.  The 
average  hourly  velocities,  however,  of  motion  in  all  directions 
are  obtainable  from  the  whole  number  of  miles  passed  over  in 
all  directions  by  the  air  in  the  course  of  a  month.  From  all 
the  data  of  this  kind  available  in  the  United  States,  and  from 
similar  data  in  Europe  and  Asia,  Loomis17  obtained  the  follow- 
ing average  velocities  in  miles  per  hour  without  regard  to 
direction : 

Jan.    Feb.     Mar.    April    May    June    July    Aug.    Sept.    Oct.    Nov.    Dec.    Year. 

United  States  (45  stations). 

"  9.69      10.13     IO-97      10.13      8.88      7.95      7.28        6.91       7.97      8.90      9.83      9.75         9.5 
Northern  Europe  (between  parallels  of  50°  and  60°). 

11.23      11.54     I1[-45      10.15      9-84      8.99      9.01        9.19      9.06     10.60     11.52     ii. 21         10.3 

.   Southern  Asia,  south  of  latitude  20°  N.  (34  stations). 
4.87      4.79     4.91      5.34     6.67     8.46     8.37     7.42     6.44     4.63     4.37     4.71        6.5 

Near  the  West  India  Islands  (7  stations). 
7.12      7.66     7.55      7.96     7.47     7.46     7.17     5.79     5.98     6.70     6.76     7.04        7.0 

From  these  results  alone  we  know  nothing  with  regard  to 
the  resultants ;  but  knowing  that  the  general  tendency  of  the 
air  in  northern  latitudes  is  easterly,  it  is  reasonable  to  suppose 
that  the  velocity  of  the  east  component  of  motion  may  be  as 
much  as  two  or  three  miles  per  hour. 

At  the  West  India  Islands  the  wind  blows  pretty  steadily 
in  a  direction  nearly  from  the  east,  except  when  disturbed  by 
cyclones,  so  that  we  may  regard  the  average  velocity  of  the 
west  component  as  being  at  least  five  miles  per  hour.  In 
southern  Asia,  on  account  of  the  great  monsoon  disturbances, 
little  can  be  inferred  from  the  results  with  regard  to  the  veloc- 
ity of  this  west  component. 

88.  For  theoretical  reasons  given  in  §  81,  the  velocity  of  the 
east  component  of  motion  at  the  earth's  surface  in  the  higher 


COMPARISONS    WITH  OBSERVATIONS.  IJI 

latitudes  of  the  southern  hemisphere  should  be  much  greater 
than  in  the  northern  hemisphere.  According  to  the  universal 
experience  of  navigators,  the  westerly  winds  of  these  latitudes 
are  nearly  incessant,  and  very  strong.  With  regard  to  the 
westerly  winds  of  the  higher  latitudes  of  both  hemispheres, 
and  especially  of  the  southern  hemisphere,  Mr.  Laughton 
says  :ld 

"  In  both  hemispheres,  to  the  north  and  south  of  the  parallel  of  35° 
or  40°  a  strong  westerly  wind  blows  with  great  constancy  all  around  the 
world.  In  the  southern  hemisphere  more  particularly  it  blows  with  a 
persistency  little  less  than  that  of  the  trade-winds,  but  with  a  strength 
which,  although  fitful,  is  very  much  greater.  From  a  fresh  strong  breeze 
at  rises  frequently  into  a  violent  gale,  and  as  such  blows  for  days  together ; 
tthe  mean  direction  being  very  nearly  west,  from  which  it  seldom  varies 
more  than  a  couple  of  points  on  either  side.  South  of  the  Atlantic, 
south  of  the  Indian  Ocean,  south  of  Australia,  in  the  higher  latitudes  of 
the  southern  Pacific,  and  to  the  southward  of  Cape  Horn,  we  find  it  still 
the  same — a  westerly  gale,  whose  strength  and  constancy  combined  have 
enabled  Australian  clippers  to  make  passages  which  seem  to  border  on 
the  fabulous." 

With  regard  io  the  winds  of  the  southern  hemisphere  it  is 

said:19 

"  The  trade-wind  system  of  the  southern  hemisphere  is  narrower  than 
Tin  the  northern,  extending  from  the  equator  to  only  about  30°  and  to 
;about  33°  in  winter.  The  system  of  westerly  winds  comprises  a  zone 
bounded  on  the  north  by  that  of  the  equatorial  winds  just  described,  and 
extends  southerly  in  the  winter  season  to  latitudes  varying  from  about 
61°  in  the  southern  Indian  Ocean  to  about  65°  or  66°  in  the  South  Pa- 
cific. Its  southern  limit  in  the  summer  season  (their  winter),  which  I 
have  ventured  to  draw  in  latitude  50°,  is  as  yet  a  matter  of  conjecture, 
no  observations  having  been  made  from  which  to  determine  it. 

"  Of  all  the  reliable  resultants  delineated  in  the  well-defined  portions 
of  the  system,  amounting  in  the  whole  to  over  250,  every  one  in  winter, 
and  all  but  seven  in  summer,  are  westerly,  and  most  of  them  are  within 
a  few  degrees  of  the  general  mean,  which  is  about  N.  75°  to  80°  W." 

89.  With  regard  to  the  annual  inequality  in  the  easterly 
;and  westerly  motions  of  the  atmosphere,  as  deduced  from  the- 
ory, §  78,  we  have  but  few  observations  having  any  bearing  on 
the  subject,  but  these  seem  to  indicate  with  some  degree  of 


132   THE    GENERAL    CIRCULATION  OF   THE   ATMOSPHERE 

certainty  that  there  really  is  such  an  inequality.  It  is  observed1 
upon  the  summits  of  Pike's  Peak  and  Mt.  Washington  that 
easterly  winds  prevail  more  in  the  summer  than  in  winter.. 
Supposing  the  magnitude  of  the  abnormal  disturbances  which 
entirely  counteract  and  reverse  the  easterly  motions  so  as  to> 
give  rise  to  easterly  winds  to  be  the  same  at  both  seasons,  it 
then  follows  that  the  easterly  motions  are  less  and  so  more  fre- 
quently reversed  in  summer  than  in  winter  by  these  abnormal 
disturbances. 

Away  up  in  the  region  of  the  cirrus  clouds  we  have  seen;, 
§  83,  that  the  easterly  velocities  are  so  great  that  they  are 
scarcely  ever  reversed  there  by  abnormal  disturbances,  or  even 
at  lower  altitudes  in  winter,  for  these  easterly  velocities  at  this, 
season  are  unusually  great.  That  the  easterly  velocities  of  the 
general  motions  of  the  upper  strata  are  greater  in  winter  than 
in  summer  may  be  inferred  from  observations  by  the  Rev. 
Clement  Ley  upon  the  motions  of  the  cirrus  clouds.  He  says: 
"  I  have  found  that  in  winter  very  local  depressions,  even  when 
deep,  scarcely  affect  the  directions  of  the  cirrus  currents  in 
their  vicinity,  the  latter  continuing  to  be  governed  by  the 
more  general  distribution  of  atmospheric  pressures.  Curiously 
enough  this  is  not  the  case  in  summer."  This  would  seem  to 
indicate  that  the  easterly  velocities  of  the  general  progressive 
motions  of  the  upper  strata  are  so  much  greater  in  winter  than 
in  summer,  that  though  they  may  be  reversed  by  the  abnormal 
gyratory  disturbances  in  the  latter  season,  they  cannot  be  in 
the  former. 

On  the  earth's  surface  the  velocities  of  resultant  motions 
are  so  small,  and  these  may  be  affected  so  much  by  monsoon 
influences,  which  have  an  annual  period,  that  it  is  difficult  to 
ascertain  from  observation  whether  there  is  an  annual  inequal- 
ity in  the  general  motions  of  the  atmosphere  at  the  earth's  sur- 
face. In  the  estimates  of  the  resultant  motions  at  the  earth's 
surface  for  numerous  stations  in  the  United  States,  Coffin 
found  the  velocities  to  be  about  twice  as  great  in  winter  as  in 
summer,  and  in  a  direction,  in  general,  a  little  to  the  north*  of" 
east.  But  this,  being  for  only  a  comparatively  small  part  of 


EFFECT  OF  MOTIONS   O.V  ATMOSPHERIC   PRESSURE.   133 

the  belt  of  easterly  motions  around  the  globe  in  the  northern 
hemisphere,  may  be  due  to  local  circumstances  of  a  monsoon 
character,  such  as  the  greater  surface  flow  of  air  into  the  Atlan- 
tic Ocean  in  the  winter  than  in  the  summer,  since  in  the  former 
season  its  temperature  is  greater,  and  in  the  latter  less,  than 
that  of  the  continent. 

It  is  seen  from  Professor  Loomis's  results,  §  87,  that  in  both 
the  United  States  and  in  northern  Europe  there  is  an  annual 
inequality  in  the  velocities  taken  without  regard  to  direction, 
and  that,  therefore,  there  is  probably  one  in  the  velocities  of 
the  resultants,  but  this  is  not  entirely  conclusive,  since  the  ab- 
normal disturbances  of  a  gyratory  character  may  be  greater  in 
winter  than  in  summer. 


EFFECT     OF    THE     GENERAL     MOTIONS     UPON    ATMOSPHERIC 

PRESSURE. 

90.  Having  investigated  the  effect  of  the  temperature 
gradient  in  producing  an  interchanging  motion  between  the 
equatorial  and  polar  regions,  and  then  the  effect  of  these,  in 
connection  with  the  deflecting  force  of  the  earth's  rotation, 
in  causing  east  and  west  components  of  motion,  the  next  step 
in  order  is  to  examine  the  effects  of  these  latter  motions,  in 
connection  with  this  same  deflecting  force,  in  causing  gradients 
of  atmospheric  pressure,  and  so  differences  of  pressure,  between 
different  parallels  of  latitude.  While  the  atmosphere,  if  it  had 
in  all  latitudes  the  same  temperature,  has  no  relative  east  or 
•west  motion,  but  only  the  absolute  motion  of  rotation  in  con- 
nection with  that  of  the  earth's  surface,  the  centrifugal  force 
of  rotation  is  just  sufficient  to  cause  the  same  ellipticity  in  the 
isobaric  surfaces  which  the  earth's  surface  has,  and  so  to  keep 
these  surfaces  parallel  with  the  earth's  surface.  But  if  the  at- 
mosphere has  an  absolute  east  component  of  motion  at  all 
altitudes  greater  or  less  than  that  of  the  earth's  surface,  or,  in 
other  words,  has  an  east  or  west  component  of  motion  relative 
to  the  earth's  surface,  then  the  atmospheric  pressure  at  the 
earth's  surface  is  no  longer  the  same  on  all  parallels  of  lati- 


134   THE   GENERAL    CIRCULATION   OF   THE   ATMOSPHERE. 

tude,  and  the  isobaric  surfaces  are  no  longer  parallel  with  the 
earth's  surface,  but  pressure  gradients  with  reference  to  this- 
surface  are  produced  in  which  the  pressure  either  increases  or 
decreases  in  a  direction  from  the  pole  toward  the  equator,  ac- 
cording as  this  component  of  motion  is  east  or  west.  If  the 
atmosphere  at  all  latitudes  had  a  relative  east  or  west  motion 
with  a  velocity  on  each  parallel  proportional  to  that  of  the 
absolute  east  velocity  of  the  earth's  surface,  then  the  ellipticity 
of  the  isobaric  surfaces  would  be  increased  or  decreased  just  as- 
much  as  that  of  the  earth's  surface  would  be  if  the  angular 
velocity  of  the  earth's  rotation  were  changed  by  the  same 
amount. 

We  have  seen,  §  71,  that  the  effect  of  the  upward  expansion 
of  the  atmosphere  due  to  the  temperature  gradient  between; 
the  equator  and  the  poles  is  to  increase  the  ellipticities  of  the 
isobaric  surfaces,  and  that  this  increase  is  in  proportion  to  the 
altitudes  of  the  strata,  and  therefore  the  east  components  of 
velocity,  represented  by  v,  which  would  give  rise  to  a  deflect- 
ing force  sufficient  to  counteract  the  force  arising  from  the 
gradient  of  this  increased  ellipticity,  §  76,  increases  as  the  alti- 
tude. But  since  these,  by  means  of  the  deflecting  forces,  are 
merely  sufficient  to  keep  the  atmosphere,  as  it  expands  up- 
ward, from  flowing  away  toward  the  poles,  they  have  no  effect 
upon  the  atmospheric  pressure  at  the  earth's  surface.  But  if, 
now,  the  atmosphere  at  the  earth's  surface  has  an  east  or  west 
component  of  motion  of  given  velocity,  that  of  all  the  strata 
above  is  changed  by  this  same  amount,  and  so  diminished 
when  the  relative  velocity  at  the  surface  is  toward  the  west. 
The  change  of  pressure,  therefore,  or  pressure  gradient,  at  the 
earth's  surface  depends  only  upon  the  east  and  wTest  compo- 
nents of  velocity  at  the  earth's  surface,  and  entirely  vanishes 
where  they  vanish,  whatever  these  velocities  may  be  at  altitudes 
above  the  earth's  surface.  At  these  altitudes,  however,  there 
are  pressure  gradients  when  there  are  no  east  or  west  compo- 
nents of  velocity  and  pressure  gradients  at  the  surface  ;  for 
since  the  deflecting  forces  arising  from  the  east  or  west  com- 
ponents of  motion  at  different  altitudes  are  just  sufficient  to> 


EFFECT  OF  MOTIONS   ON  ATMOSPHERIC  PRESSURE.    135 

counteract  those  of  the  temperature  gradients,  these  remain 
and,  as  we  have  seen,  §  71,  increase  with  increase  of  altitude. 

What  precedes  is  based  upon  the  hypothesis  that  there  is 
no  interchanging  motion  of  the  atmosphere  between  the  equa- 
torial and  polar  regions — or  at  least,  if  there  is  such  a  motion, 
no  sensible  force  or  pressure  gradient  is  required  to  overcome 
the  frictional  resistances  to  this  motion  and  to  maintain  it. 
But  we  have  seen  that  the  east  or  west  components  of  motion 
where  there  is  friction  cannot  be  maintained  without  the  other ; 
and  so  wherever  there  is  polar  motion,  as  in  the  upper  strata, 
the  east  components  of  velocities  must  be  a  little  less ;  and 
where  there  is  equatorial  motion,  as  in  the  lower  strata  mostly, 
they  must  be  greater,  or  if  the  components  of  motion  are 
toward  the  west,  less,  than  those  which  would  give  rise  to  a 
deflecting  force  which  would  exactly  counteract  that  of  the 
temperature  gradient. 

91.  The  general  expression  of  the  barometric  gradient  G, 
corresponding  to  any  given  velocity  s  in  any  direction,  so  far 
as  it  depends  upon  the  deflecting  forces  corresponding  to  this 
velocity,  is  given  in  §  57.  In  the  special  case  now  being  con- 
sidered, s  becomes  v,  the  east  component  of  relative  velocity 
of  the  atmosphere,  and  we  therefore  have  here 

P     T 

G  —  0.1571*'  sin  l-p  •  ~  . 
*i     * 

By  substituting  for  v  its  general  expression,  §  77,  in  a  func- 
tion of  the  temperature  gradient  A-r  and  of  the  east  component 
of  velocity  at  the  earth's  surface  v0 ,  we  get 

p     T 
G  —  o.i57i(V0  sin  /+  246.4/2/77-)  ~-  •  ~  - 

*9         * 

From  this  expression  of  the  barometric  gradient  we  arrive 
at  the  same  conclusion  as  in  the  preceding  paragraph,  namely, 
that  the  pressure  gradient  at  the  earth's  surface,  so  far  as  it 
depends  merely  upon  the  east  or  west  components  of  velocity 
at  the  earth's  surface,  vanishes  where  they  vanish.  For  at  the 
earth's  surface  we  have  h  equal  to  o,  and  as  P  there  is  generally 


136   THE   GENERAL    CIRCULATION  OF    THE   ATMOSPHERE. 

very  nearly  the  same  as  P0 ,  we  always  have  in  this  special  case, 
very  nearly, 

T 
GQ  =  0.1571^  sin  /--• 

It  will  be  remembered  that  G  is  the  change  of  atmospheric 
pressure  in  millimeters  of  mercury  in  the  distance  of  one  de- 
gree of  a  great  circle  of  the  earth,  in  a  direction  at  right  angles 
to  the  direction  of  motion,  in  case  the  rate  of  change  should 
continue  the  same  through  so  great  a  range.  From  this  ex- 
pression we  may  infer  that  in  the  northern  hemisphere  and  in 
the  higher  latitudes,  where  z/0  is  positive,  the  atmospheric  pres- 
sure increases  from  the  pole  toward  the  equator  to  about  the 
parallel  of  35°  or  30°,  where  VQ  vanishes  and  changes  sign  ;  but 
between  this  parallel  and  the  equator,  where  VQ  is  negative  or 
west,  the  pressure  decreases.  In  the  southern  hemisphere  the 
gradient  is  reversed  on  account  of  the  change  of  sign  of  sin  /. 
Hence  immediately  south  of  the  equator,  where  VQ  is  negative, 
we  have  increasing  pressure  to  about  the  parallel  of  30°,  where 
^0  vanishes  and  changes  sign,  becoming  positive  again  ;  after 
which  the  pressure  decreases  again  to  the  pole,  and  very  rapidly 
in  the  middle  latitudes  where  the  positive  values  of  v0  are  very 
large  (§  88).  At  the  equator,  where  sin  /vanishes,  the  gradient 
also  vanishes,  and  there  is  here  consequently  a  minimum  pres- 
sure. The  pressure,  therefore,  in  both  hemispheres  increases  in 
the  higher  and  middle  latitudes  in  going  from  the  poles  toward 
the  equator  to  about  the  parallel  of  30°  or  35°  where  there  is  a 
maximum  pressure,  and  then  decreases  to  the  equator  where 
there  is  a  minimum.  The  gradients,  however,  in  approaching 
the  equator  from  either  side,  are  small  on  account  of  the 
small  value  of  sin  /  there,  and  consequently  the  equatorial  de- 
pression is  small.  There  is  then,  or  would  be  if  they  were  not 
interfered  with  by  abnormal  disturbances,  a  zone  of  high  pres- 
sure in  each  hemisphere  around  the  globe  with  its  maximum 
near  the  parallel  of  30°,  an  equatorial  zone  of  low  pressure  with 
its  minimum  at  the  equator,  and  an  area  of  low  pressure  around 
each  pole  with  its  minimum  at  the  pole. 


EFFECT  OF  MOTIONS  ON  ATMOSPHERIC  PRESSURE.    137 

It  seems  difficult  for  some  to  conceive  how  the  equatorial 
•depression  can  be  due  to  the  westerly  motion  of  the  atmos- 
phere, since  this  motion  prevails  at  the  earth's  surface  and  in  the 
lower  strata  of  the  atmosphere  only,  while  above  the  motion  is 
easterly.  But  it  has  been  shown  that  in  the  case  of  no  east  or 
west  component  of  motion  at  the  earth's  surface  the  east  com- 
ponents are  necessary  to  keep  the  air  above  from  flowing  away 
from  the  equatorial  region,  and  thus  from  diminishing  the  pres- 
.sure  there.  If,  then,  the  lower  stratum  next  the  earth's  surface 
has  a  west  component  of  motion,  we  have  seen  that  the  veloci- 
ties of  all  the  strata  above  to  the  top  of  the  atmosphere  have 
their  velocities  changed  by  the  same  amount,  and  the  effect 
upon  the  pressure  at  the  earth's  surface  is  precisely  the  same 
as  if  there  were  no  temperature  gradient  and  no  east  compo- 
nents of  velocity  above,  and  all  the  strata  from  bottom  to  top 
should  receive  a  west  component  of  motion. 

92.  According  to  the  preceding  approximate  general  ex- 
pression of  G,  it  is  seen  that  the  pressure  gradient  at  the  earth's 
surface,  where  h=o,  is  positive  where  v0  sin  /is,  and  vanishes  and 
changes  sign  at  the  latitude  where  v0  does.  The  greatest  pres- 
sure, therefore,  at  the  earth's  surface  is  on  this  parallel,  or  nearly. 
But  at  any  altitude  above  the  earth's  surface  the  expression  of 
G  vanishes  at  some  latitude  nearer  the  equator,  since  after  v0  be- 
•comes  negative,  the  term  in  the  parenthesis  depending  upon  h 
being  always  positive  in  the  northern  hemisphere,  and  in  either 
of  a  contrary  sign  to  that  of  v0  sin  /  in  these  latitudes,  the  ex- 
pression only  vanishes  where  the  negative  value  of  v0  sin  /  is 
equal  to  the  part  in  the  parenthesis  depending  upon  h,  and 
hence  the  greater  h  is,  the  nearer  the  equator  is  the  latitude 
where  G  vanishes  and  the  pressure  is  a  maximum.  In  order 
to  make  G  vanish,  the  following  conditions  must  be  satisfied : 

2/0  sin  /  +  246.4^ AT:  =  o. 

The  altitude  on  any  given  latitude  where  this  condition  is 
satisfied  of  course  depends  upon  the  value  of  z/0,  but  for  some 
distance  toward  the  equator  from  the  parallel  where  v0  vanishes, 
the  term  %  sin  /  increases  although  sin  /  diminishes ;  and  hence 


138   THE   GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

the  greater  the  altitude  the  nearer  the  equator  is  the  latitude- 
where  G  vanishes  and  the  maximum  pressure  occurs  in  going 
horizontally  toward  the  equator.  The  values  of  VQ  ,  however,, 
corresponding  to  the  different  latitudes  or  values  of  sin  /,  may 
be  so  small  that  at  and  above  a  given  altitude  the  second  term 
above  may,  for  all  latitudes,  be  greater  than  the  negative  value 
of  the  first  one,  and  then  the  expression  is  positive  and  does, 
not  vanish  at  all,  except  at  the  equator,  where  both  sin  /  and 
AT:  vanish ;  and  therefore,  above  a  given  altitude  and  at  all 
higher  altitudes,  the  maximum  pressure,  in  going  horizontally 
toward  the  equator,  is  only  reached  at  the  equator,  and  at 
these  altitudes  there  is  a  continuous  gradient  of  pressure  in- 
creasing from  the 'pole  to  the  equator.  With  no  value  of  VQ  on 
any  parallel,  that  is,  with  no  east  or  west  components  of  mo- 
tion at  the  earth's  surface,  we  have  seen  there  would  be  no 
pressure  gradient  at  the  earth's  surface,  so  far  as  it  depends 
upon  v  and  the  deflecting  forces,  but  at  any  altitude  above  the 
surface  there  would  be  a  gradient  of  increasing  pressure  from> 
the  pole  to  the  equator,  and  this  at  great  altitudes  is  so  large,, 
that  the  west  component  of  motion  of  the  atmosphere  at  the 
earth's  surface,  and  the  consequent  change  of  velocities  by  the 
same  amount  at  all  altitudes,  are  not  sufficient,  by  means  of  the 
deflecting  forces,  to  reverse  this  gradient  except  in  the  lower- 
strata  of  the  atmosphere  up  to  a  certain  altitude.  Above  this 
altitude,  therefore,  there  is  no  barometric  minimum  at  the 
equator,  but  a  maximum,  arising  from  the  gradual  nearer 
approach  of  the  maxima  on  each  side  towards  the  equator  as 
the  altitude  increases. 

It  must  be  always  borne  in  mind  that  the  preceding  rela- 
tions are  not  strictly  correct,  but  only  approximately  so,  since 
the  value  of  v,  §  77,  which  has  been  used  in  obtaining  the  pre- 
ceding expression  of  G  is  approximate  only,  being  the  true  ex- 
pression in  the  case  of  no  friction,  in  which  case  there  is  no 
necessity  for  an  interchanging  motion  between  the  equator  and 
the  poles,  but  is  in  all  cases  a  limit  beyond  which  the  value  of 
v  cannot  go  and  of  which  it  must  fall  a  little  short,  and  the: 
greater  the  amount  of  friction  to  be  overcome  the  more  so. 


EFFECT  OF  MOTIONS  ON  ATMOSPHERIC  PRESSURE.    139 

93.  From  what  precedes,  there  is,  at  the  earth's  surface,  an 
area  of  low  pressure  around  each  pole  with  its  minimum  at 
the  pole,  a  zone  of  high  pressure  hi  each  hemisphere  with  its 
maximum  about  the  parallel  of  30°,  and  an  equatorial  zone  of 
slightly  diminished  pressure  with  the  minimum  at  the  equator. 
And  this  same  arrangement  exists  in  the  lower  strata  of  the  at- 
mosphere up  to  a  considerable  altitude, — except  that  the  polar 
depressions  are  greater  and  the  parallel  of  maximum  pressure 
comes  nearer  the  equator  as  the  altitude  is  increased,  until  at 
a  certain  altitude  the  two  maxima  combine  to  form  a  maximum 
pressure  at  the  equator.  Instead,  then,  of  the  isobaric  surfaces 
being  elliptical,  and  having  an  increasing  ellipticity  in  propor- 
tion to  the  altitude,  as  represented  in  Fig.  3,  they  have,  in 
consequence  of  the  east  and  west  components  of  motion  of  the 
atmosphere  at  the  earth's  surface,  steeper  gradients  in  the 
higher  and  middle  latitudes,  a  bulging  up  nearer  the  equator, 
and  in  the  lower  strata  a  minimum  altitude  at  the  equator,  as 
represented  in  Fig.  4,  in  which  the  intersections  of  the  line  eo- 
with  the  isobaric  surfaces  indi- 
cate the  latitudes,  at  the  several 
altitudes,  where  the  pressures  are 
the  greatest  and  where  the  east 
components  of  velocity  vanish, 
change  sign,  and  become  west 
components  of  velocity.  The 
actual  form  and  position  of  the 
line  eo,  since  they  depend  upon  the 
west  components  of  motion  at 
the  earth's  surface,  and  the  tem- 
perature gradient,  are  quite  un- 
certain toward  the  equator. 

Before  the  exploring  expeditions  led  by  Captain  Wilkes 
and  Sir  James  Ross  it  was  pretty  generally  thought  that  the 
barometric  pressure  at  sea-level  in  all  parts  of  the  earth  is 
nearly  or  quite  the  same,  and  about  30  inches.  From  the 
barometric  observations  of  these  expeditions  it  was  first  clearly 


140   THE    GENERAL    CIRCULATION   OF   THE  ATMOSPHERE. 


shown    that    this   is  by  no   means  the   case.       Says  Captain 
Wilkes:35 

"The  most  remarkable  phenomenon  which  our  observations  have 
shown  is  the  irregular  outline  of  the  atmosphere  surrounding  the  earth 
as  indicated  by  the  pressure  upon  the  measured  column  at  different  parts 
of  the  surface.  Our  barometrical  observations  show  a  depression  within 
the  tropics,  a  bulging  in  the  temperate  zone,  again  undergoing  a  depres- 
sion on  advancing  towards  the  arctic  and  antartic  circles." 

Says  Sir  James  Ross:36 

"  Our  barometrical  experiments  appear  to  prove  that  the  atmospheric 
pressure  is  considerably  less  at  the  equator  than  near  the  tropics ;  and  to 
the  south  of  the  tropic  of  Capricorn,  where  it  is  greatest,  a  gradual  diminu- 
tion occurs  as  the  latitude  is  increased,  as  will  be  shown  from  the  follow- 
ing table,  derived  from  hourly  observations  of  the  height  of  the  column 
•of  mercury  between  the  2oth  of  November,  1839,  and  tne  3ist  of  July, 
1843." 

EXTRACT  FROM  ROSS'S  TABLE. 


Latitude. 

Pressure, 
Inches. 

.  Latitude. 

Pressure, 
Inches. 

Latitude. 

Pressure, 
Inches. 

Equator. 

29.974 

42°  53' 

29.950 

55°  52' 

29.360 

13°    o'S. 

30.016 

45      o 

29.664 

60     o 

29.114 

22    17 

30.085 

49     8 

29.467 

66     o 

29.078 

34   43 

30.023 

5i    33 

29.497 

74     o 

28.928 

54    26 

29-347 

So  strange  and  unaccountable  did  these  phenomena  appear 
before  the  discovery  of  the  deflecting  force  of  the  earth's  rota- 
tion, that  Espy  said  :  "  Unless  I  have  positive  testimony  to  the 
fact,  I  shall  not  believe  that  the  barometer  stands  lower  at  the 
level  of  the  sea  in  the  southern  hemisphere  than  in  the  north- 
ern, only  in  regions  where  great  snows  or  rains  prevail,  and  only 
while  they  do  prevail."  This  was  upon  the  theory  that  great 
barometric  depressions  are  caused  by  a  great  quantity  of 
•aqueous  vapor  in  the  atmosphere. 

94.  Since  the  whole  vertical  circulation  and  the  east  and 
'west  components  of  motion,  and  the  deflecting  forces  arising 
.from  them,  from  which  result  the  polar  and  equatorial  depres- 


EFFECT  OF  MOTIONS  ON  ATMOSPHERIC  PRESSURE.    141 

sions  and  the  zones  of  high  pressure  near  the  tropics,  depend 
upon  the  temperature  gradients  between  the  equator  and  the 
poles,  there  must  be  greater  polar  depressions  of  the  isobaric 
surfaces  and  a  greater  bulging  up  in  the  middle  and  lower  lati- 
tudes in  winter  than  in  summer,  since  the  temperature  gradients 
are  much  greater  in  the  former  season  than  in  the  latter,  espe- 
cially in  the  northern  hemisphere,  where  they  are  more  than 
twice  as  great  in  January  as  in  July.  There  must,  then,  be  an 
annual  inequality  of  atmospheric  pressure  from  this  cause,  such 
that  the  pressure  is  greater  in  the  winter  than  in  the  summer 
of  each  hemisphere  in  the  middle  and  lower  latitudes,  and  the 
reverse  in  the  polar  regions. 

But  for  another  reason,  also,  there  is  an  annual  oscillation 
of  pressure.  During  the  winter  of  each  hemisphere  the  atmos- 
phere becomes  much  colder  than  it  is  in  the  other  hemisphere, 
and  consequently  its  volume  considerably  less,  so  that  the  iso- 
baric surfaces  lie  lower  in  the  colder  hemisphere  than  in  the 
other.  There  is,  consequently,  a  pressure  gradient  above  by 
which  the  air  of  the  higher  strata  flows  from  the  warmer  hemi- 
sphere to  the  colder  one  and  increases  the  mass  and  pressure  of 
the  atmosphere  there  a  little,  and  diminishes  them  by  the  same 
amount  in  the  warmer  hemisphere,  until  there  is  a  reverse  gra- 
dient formed  in  the  lower  strata  which  gives  rise  to  a  counter 
flow  of  air  below  from  the  colder  to  the  warmer  hemisphere. 
There  is,  in  this  way,  an  interchanging  motion  originated  and 
maintained  between  the  two  hemispheres,  just  as  there  is  be- 
tween the  warm  equatorial  and  cold  polar  region  of  each  hemi- 
sphere, as  has  been  describee!  in  §  72.  But  the  interchange 
between  the  two  hemispheres  is  kept  up  with  greater  facility, 
since  there  are  no  east  components  of  motion  at  and  near  the 
equator,  where  the  temperature  and  pressure  gradients  in  this 
case  and  the  velocity  of  flow  are  the  greatest,  to  give  rise  to 
counter  deflecting  forces,  as  there  are  in  the  middle  latitudes 
in  the  other  case,  but  the  whole  temperature  and  pressure 
gradients  are  brought  to  bear  in  maintaining  the  flow  of  air 
above  from  the  warmer  to  the  colder  hemisphere,  and  the  con- 
trary in  the  lower  strata. 


I42    THE   GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

As  there  is  an  annual  inversion  of  the  temperature  conditions 
•which  give  rise  to  and  maintain  these  interchanging  motions 
between  the  two  hemispheres,  so  there  is  also  one  in  the  pres- 
sure gradients  at  the  earth's  surface  and  in  the  lower  strata, 
.arising  from  the  flow  of  air  above  from  the  warmer  to  the 
colder  hemisphere,  and  in  the  slight  increase  of  pressure  there 
and  corresponding  diminution  in  the  other  hemisphere,  to  cause 
this  gradient.  There  is  therefore  a  little  more  air,  and  conse- 
quently a  little  greater  pressure  at  the  earth's  surface,  in  each 
hemisphere  in  winter  than  in  summer,  and  this  causes  a  slight 
annual  inequality  of  pressure,  the  pressure  being  the  greatest 
in  each  hemisphere  in  the  midwinter  of  that  hemisphere.  The 
greatest  effect  of  this  latter  cause  of  the  annual  inequality  is  at 
the  poles,  whereas  in  the  other  case  the  pressure  is  increased 
an  winter  in  the  middle  latitudes,  but  diminished  in  the  polar 
regions.  It  is  the  resultant  of  these  two  effects  which  is  ob- 
served. 

95.  An  annual  inequa'ity  of  pressure  is  observed  on  nearly 
every  part  of  the  globe,  but  on  account  of  various  local  disturb- 
ances of  pressure,  this,  as  the  temperature,  is  not  the  same  at 
all  places  on  the  same  parallel.  But  by  obtaining  the  normal 
pressures  of  latitude,  as  those  of  temperature,  by  taking  the 
average  of  observed  values  all  around  the  globe  on  each 
parallel,  we  eliminate  the  effects  of  these  local  disturbances.  In 
this  way  the  results  given  in  the  following  table  have  been  ob- 
tained.8 These  results,  however,  must  be  regarded  as  being  only 
approximate,  since  the  material  on  hand  then,  more  than  ten 
years  ago — was  insufficient  for  accurate  results — since  there  was 
a  great  deficiency  of  observations  over  nearly  all  parts  of  the 
•great  oceans.  It  is  much  to  be  regretted  that  the  work  has 
not  been  repeated  with  the  now  much  greater  material  on  hand 
for  such  a  purpose. 

In  the  following  table  are  given  for  the  earth's  surface  the 
normal  barometic  pressure  of  latitude,  P\  the  barometric  gra- 
dient, G',  and  the  annual  variations,  AP  and  AG,  for  each 
fifth  degree  of  latitude,  so  far  as  there  were  any  available  obser- 
vations. 


EFFECT  OF  MOTIONS  ON  ATMOSPHERIC  PRESSURE.    143 


Latitude. 

Annual  Mean. 

Annual  Inequality. 

P 

G 

" 

AC 

mm. 

mm. 

mm. 

mm. 

+  80° 

760.5 

.... 

—  0.06 

.... 

75 

760.0 

—  O.ig 

+  0.19 

+  0.04 

70 

758.6 

—  0.14 

0.36 

0.05 

65 

758.2 

+  0.01 

0.63 

O.O6 

60 

758.7 

0.15 

0.97 

0.06 

55 

759-7 

O.2O 

.26 

0.05 

50 

760.7 

0.18 

.41 

0.03 

45 

761.5 

0.15 

•53 

0.02 

40 

762.0 

+  0.07 

.61 

+  0.01 

35 

762.4 

—  0.03 

.66 

O.OO 

30 

761.7 

0.18 

.66 

—  0.01 

25 

760.4 

0.25 

.61 

0.03 

20 

759-2 

O.2I 

.41 

O.O6 

15 

758-3 

0.13 

-05 

0.09 

10 

757-9 

—  0.03 

+  0.50 

O.II 

4-5 

758.0 

+  O.OI 

—  0.05 

0.12 

0 

758.0 

0.04 

0.63 

0.12 

-  5 

758.3 

O.II 

1.18 

O.II 

10 

759-1 

O.2O 

1.70 

0.08 

15 

760.2 

0.26 

2.OO 

0.06 

20 

761.7 

0.29 

2.22 

—  O.O3 

25 

763.2 

+  0.18 

2.36 

O.OO 

30 

763-5 

—  0.08 

2.22 

+  0.03 

35 

762.4 

0.30 

1.85 

0.06 

40 

760.5 

0.51 

I.4I 

0.07 

45 

757-3 

0.73 

I.OO 

0.09 

50 

753-2 

0.91 

—  0.50 

O.IO 

55 

748.2 

0.97 

0.00 

+  0.10 

60 

743-4 

0.83 

65 

739-7 

—  0.56 

-70 

738.0 

From  the  preceding  table  it  is  seen  that  the  mean  normal 
pressure  of  latitude  is  greatest  in  the  northern  hemisphere 
about  the  parallel  of  3-5°,  and  in  the  southern  hemisphere  a 
little  nearer  the  equator,  about  the  parallel  of  30°,  and  that 
there  is  an  equatorial  depression  and  a  polar  one  in  each  hemi- 
sphere, in  accordance  with  the  theoretical  deductions  of  §  93. 
The  mean  pressure  gradient  is  greater  in  the  southern  than  in 
the  northern  hemisphere,  and  is  especially  large  in  the  vicinity 
of  the  parallel  of  55°  S.,  as  it  should  be  according  to  theory 
-and  the  theoretical  expression  of  G,  §  91,  since  the  east  and 
west  components  of  velocity,  or  values  of  v0 ,  are  greater  in  the 


144  THE    CENEKAL    CIRCULATION   OF    THE   ATMOSPHERE. 

former  than  in  the  latter,  and  the  east  component  is  especially 
large  at  and  near  the  parallel  of  55°  (§  88).  The  pressure  gra- 
dients, being  reckoned  on  the  meridian  from  the  north  toward 
the  south  pole,  have  contrary  signs  generally  on  corresponding 
parallels  of  the  two  hemispheres. 

96.  The  coefficients  of  the  annual  inequalities  AP  and  AG 
in  the  preceding  table,  added  to  the  mean  pressure  and  mean 
pressure  gradient  for  the  year,  give  the  mean  pressure  and 
mean  pressure  gradient  for  January,  and  subtracted,  those  for 
July.  It  is  seen,  therefore,  that  the  pressures,  by  observation, 
are  greatest  in  each  hemisphere  during  the  winter  of  that 
hemisphere,  except  very  near  each  pole,  as  required  by  theory, 
§  94.  The  annual  inequality  of  pressure,  by  the  theory,  is  the 
result  of  two  separate  effects,  which  in  the  middle  and  lower 
latitudes  of  each  hemisphere  are  both  in  the  same  direction,, 
tending  to  increase  the  pressure  in  the  winter  season  of  the 
hemisphere.  But  the  effect  which  arises  from  the  bulging  up 
of  the  isobaric  surfaces  in  the  middle  and  lower  latitudes, 
and  a  corresponding  depression  in  the  polar  latitudes,  has  a 
contrary  sign  in  the  polar  latitudes,  and  seems  to  be  of  such  a 
magnitude  as  to  more  than  counteract  the  other  effect,  and  hence 
in  these  latitudes  the  annual  inequality  is  reversed,  and  the  baro- 
metric pressure  is  less  during  the  winter  than  the  summer  sea- 
son. There  is,  consequently,  a  parallel  very  near  the  pole  in 
the  northern  hemisphere,  but  near  the  parallel  of  55°  m  the 
southern,  where  there  is  no  annual  inequality  of  barometric 
pressure. 

The  annual  inequality  of  pressure  is  greater  in  the  southern 
than  in  the  northern  hemisphere,  and  the  maximum  nearer  the 
equator,  being  in  the  southern  hemisphere  on  the  parallel  of 
25°,  while  in  the  northern  it  is  about  the  parallel  32°. 5.  This 
arises  from  the  greater  amount  of  water  surface  and  conse- 
quently less  amount  of  frictional  resistance  to  the  east  and  west 
components  of  motion  at  the  surface  in  the  southern  hemi- 
sphere than  in  the  other.  For  since,  on  this  account,  there  is  a 
greater  mean  bulging  up  of  the  strata  of  equal  pressure  in  the 
middle  and  lower  latitudes,  and  depression  of  them  in  the 


EAST  VELOCITIES  DEDUCED  FROM  PRESSURE  GRADIENT.  145 

polar  latitudes,  corresponding  to  the  mean  temperature  gra- 
dients of  the  year,  in  the  southern  than  in  the  northern  hemi- 
sphere, the  annual  inequality  of  pressure  corresponding  to  the 
annual  inequality  of  temperature  must  likewise  be  greater  in 
the  former  than  in  the  latter,  for  the  effect  of  the  annual 
reversion  of  the  interchanging  motions  between  the  two 
hemispheres,  upon  the  east  components  of  motion  of  the 
atmosphere,  and  consequently  upon  the  pressures,  must  be 
the  greater  in  the  hemisphere  which  has  the  more  water  sur- 
face. 

EAST    VELOCITIES  DEDUCED    FROM    PRESSURE  AND    TEMPERA- 
TURE  GRADIENTS. 

97.  To  any  pressure  gradient  G  at  the  earth's  surface,  or 
any  altitude  above  it,  there  is  a  corresponding  velocity  v  of 
east  or  west  component  of  motion,  §  91,  so  that  if  one  is  known 
the  other  may  be  approximately  computed.  We  can  more 
easily  obtain  from  observation  the  normal  gradients  of  pressure 
than  the  east  or  west  component  of  wind  velocity,  and  there- 
fore this  component  can  be  more  readily  obtained  from  the  ob- 
served pressure  gradients  than  directly  from  observation.  For 
instance,  taking  the  parallel  of  50°  N.  for  an  example,  we  find  in 
the  preceding  table  the  normal  gradient  of  pressure  at  the 
earth's  surface  is  0.18  mm.  With  this  value  of  G  and  the  value 
of  sin  50°,  Table  V,  we  readily  get  from  the  special  expression 
of  G0  in  §  91,  v0  =  1.5  m.  as  the  east  component  of  velocity  at 
the  earth's  surface.  Now  from  the  temperature  differences  for 
10°  preceding  and  following  the  latitude  of  50°  for  the  mean 
of  the  year,  §  68,  we  get  approximately  the  gradient  Ar  = 
(7-9  +  7-3)/20  =  °-76.  This  is  for  the  distance  of  one  degree,  in> 
which  case  the  numerical  coefficient  0.00221  must  be  used  in 
the  expression  of  v  in  §  77.  With  these  values  of  v0  and  AT 
this  expression  gives  for  the  altitude  h  —  1000  meters,  v  = 
1.5  +  2.2  =  3.7  m.  for  the  value  of  the  east  component  of  mo- 
tion, in  meters  per  second,  at  the  height  of  one  kilometer.  For 
any  other  altitude  the  last  term  would  be  increased  in  propor- 
tion. Thus,  for  an  altitude  of  5  kilometers  we  should  have 


146   THE   GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 


<v  —  1.5  x  2.2  X  5  =  12.5  in  meters  per  second.      Multiplying 
by  3.6,  we  get  v  =  45  in  kilometers  per  hour. 

98.  Somewhat  in  the  same  manner,  the  following  table  of 
values  of  v  in  kilometers  per  hour  have  been  computed  for  the 
mean  of  the  year,  and  for  January  and  July,  for  each  fifth  de- 
gree of  latitude,  except  near  the  equator  and  the  poles,  where 
the  formula  and  the  data  are  too  uncertain.  The  temperature 
gradients,  however,  were  obtained  by  another  method,  more 
accurate  than  that  used  above.8 


Lcititu.de 

V 

Mean  of  the  Year 

January. 

July. 

km. 

km. 

km. 

+  75 

—  4.4  +  4.8    / 

i 

—  1.9  +  4.4   / 

t 

—  5-7  +  5-1    J 

70 

—  3-3       6.6 

-    LI        7.5 

4-8       5-8 

65 

+  0.2         7-7 

+    1.6        9.6 

—1.2         5.9 

60 

3.9    8.3 

5-5      10.9 

+  2.3       5-6 

\         55 

5-5       8.5 

7.0     ii.  6 

4-o       5.4 

50 

5.4       8.6 

6.4      12.  I 

4.4       5-i 

45 

4.9       8.8 

5-5       126 

4.1       5.0 

40 

+  2.6       9.0 

+  2.8     12.9 

+  2.4      4.8 

1          35 

-1.2         9.3 

—  i.o     13.8 

—  1.4      4.6 

30 

8.6       9.5 

9.1    14.7 

8.1       4.3 

25 

14-4       9-4 

16.0     15.2 

12.2         3.6 

20 

15-1       9-° 

2O.  2      15.6 

ii.  7       2.4 

+  15 

12.5       5.6 

21.8     10.5 

3.8       0.6 

—  15 

25.0       8.2 

18.7     4.9 

31.0     ii.  7 

2O 

20.9       7.8 

18.8       5.8 

23.0     10.0 

25 

—  10.3       7.6 

—  10.4       6.6 

—  16.1       8.7 

r     30 

+    3-8       7-5 

+    2.3       7.3 

+    5-2       7-8 

>         35 

12.4       7.4 

10.  0         7.8 

14.4       7.1 

40 

18.7       7.4 

16.0      8.2 

21.4      6.7 

45 

24.0       7.4 

21.0      8.6 

27.0      6.4 

50 

27-5       7-5 

24.5       8.9 

30.5       6.1 

55 

27-3       7-5 

+  24.6  +  9.1 

30.0       5.9 

60 

+  21.9+7.5 

By  adding  together  the  two  parts  of  the  value  of  v,  the  first 
being  v0 ,  the  value  of  v  at  the  earth's  surface,  where  k—Q,  and 
depending  upon  and  deduced  from  the  pressure  gradient  there, 
and  the  second  depending  upon  the  altitude  hr  we  get  the  east 
component  of  velocity  v  in  kilometers  per  hour  at  any  given 
altitude  h  in  kilometers.  But  by  reducing  the  first  part  to 


IE  AST  VELOCITIES  DEDUCED  FROM  PRESSURE  GRADIENT.  147 

miles  by  multiplying  by  0.62  we  get  the  result  in  miles  per  hour 
if  the  value  of  h  is  given  in  miles.  For  instance,  on  the  paral- 
lel of  50°  N.  and  for  altitude  h  =  5  kilometers,  we  have  for  the 
mean  of  the  year  v  —  5.4  +  8.6  X  5  =  48.4  kilometers  per 
hour.  This  'differs  a  little  from  the  result  of  the  preceding 
computation  with  the  temperature  gradient  deduced  approxi- 
mately from  first  differences  merely  where  the  intervals  are  ten 
degrees  of  latitude.  In  like  manner,  by  reducing  the  first  part 
to  miles,  we  have  i/=  3.3  +  8.6  X  5  =  46.3  miles  per  hour  for 
the  east  component  of  velocity  at  the  altitude  h  =  5  miles. 

In  the  same  way  we  get,  on  this  same  parallel  of  latitude, 
v  =  4.0  +  12. i  X  5  =64-$  miles  per  hour  for  the  approximate 
«ast  component  of  velocity  of  the  air  at  the  altitude  of  5  miles 
in  January,  and  v  =  2.8  -f-  5.1  X  5  =  28.3  miles  per  hour  for 
this  velocity  in  July.  Hence  the  east  component  of  velocity  at 
considerable  altitudes  is  more  than  twice  as  great  in  January 
as  in  July  on  this  latitude,  and  the  same  is  true  of  the  middle 
and  higher  altitudes  generally  in  the  northern  hemisphere,  as 
has  already  been  deduced  in  a  general  way  in  §  78.  At  and 
near  the  earth's  surface,  however,  where  the  value  of  v  depends 
mostly  upon  v0 ,  and  especially  in  the  lower  latitudes  where  the 
value  of  v0  is  considerable  and  negative,  the  ratio  between  Jan- 
uary and  July  is  a  little  different,  since  it  depends  mostly  or 
•entirely  upon  that  of  f0  for  the  two  extremes  of  the  seasons,  in 
which  the  uncertainty  of  friction  corresponding  to  different 
velocities  comes  in,  so  that  this  part,  as  deduced  from  the 
barometric  gradients  of  pressure,  does  not  quite  have  the  same 
relations  between  the  different  seasons  as  the  temperature 
gradients. 

In  the  lower  latitudes,  where  there  is  a  west  component  of 
motion  at  the  earth's  surface,  we  have  VQ  negative,  and  so  these 
west  components  of  velocity  are  diminished  above  by  the 
quantity,  for  the  different  altitudes,  in  the  preceding  table 
depending  upon  h,  so  that  at  certain  altitudes  they  become 
reversed  and  become  east  components  of  velocity.  Thus  on 
the  parallel  of  20°  N.  we  have,  for  the  mean  of  the  year,  v  = 
— 15.1  -4-Q.O/t.  It  is  readily  seen  that  in  order  to  make  v  van- 


148   THE    GENERAL    CIRCULA  TION  OF   THE  A  TMOSPHERE. 

ish  we  must  have  h  =  15.1/9.0=  1.7  km.  nearly  for  the  alti- 
tude where  v  vanishes  and  changes  sign,  and  where,  consequent- 
ly, there  is  no  east  or  west  component  of  motion  of  the  air.  It 
is  seen  from  the  table  that  this  altitude  differs  for  different 
parallels  of  latitude  and  the  different  seasons, of  the  year,  being 
very  small  at  the  parallel  of  30°  and  gradually  increasing  toward 
the  equator,  and  being  also,  at  and  within  the  tropics,  very 
much  greater  in  July  than  in  January. 

In  the  southern  hemisphere  on  the  parallel  of  50°  we  have 
for  the  mean  of  the  year  at  the  altitude  of  5  kilometers,  v  = 
27.5  -f-  7.5  X  5  =  65  kilometers  for  the  east  component  of  veloc- 
ity of  the  air  per  hour.  This  is  considerably  greater  than  that 
obtained  above  for  the  same  latitude  and  altitude  in  the  north- 
ern hemisphere,  due  to  the  greater  east  component  of  velocity 
at  the  earth's  surface  for  reasons  already  explained.  The  differ- 
ences between  January  and  July,  as  given  by  this  table,  are 
very  small  in  comparison  with  those  of  the  northern  hemisphere 
on  account  of  the  comparatively  small  differences,  generally,  in 
the  temperatures,  as  may  be  seen  from  the  table  of  §  68. 

99.  We  have  seen  that  the  maximum  atmospheric  pressure, 
§  92,  in  going  at  any  altitude  horizontally  toward  the  equator, 
occurs  where  v  =  o  ;  and  hence  the  latitude  of  greatest  pressure 
at  any  given  altitude  is  readily  ascertained  approximately  from 
a  mere  inspection  of  the  preceding  table,  it  being  on  the  parallel 
which  makes  the  expression  of  v  vanish  at  the  given  altitude. 
Thus,  in  the  northern  hemisphere,  for  the  mean  of  the  year,  at 
the  altitude  of  one  kilometer,  the  latitude  on  which  this  condi- 
tion is  satisfied  is  a  little  below  30°,  while  at  the  earth's  surface 
the  greatest  pressure  is  about  36°.  At  greater  altitudes  this 
latitude  is  still  nearer  the  equator,  but  the  exact  latitude  be- 
comes more  uncertain  on  account  of  the  uncertainty  of  the 
data,  and  the  small  changes  of  pressure  with  a  given  change  of 
latitude  at  these  altitudes.  Above  a  certain  altitude,  it  is  read- 
ily seen,  so  far  as  the  table  extends,  that  the  condition  cannot 
be  satisfied,  and  hence  east  velocities  prevail  above  this  altitude. 

From  the  applications  which  have  been  made  of  the  pre- 
ceding table,  both  to  the  east  and  west  component  of  velocity 


SURFACE    WINDS,   CALMS,  AND   CALM-BELTS.  149 

of  the  air  and  to  the  pressures,  it  is  seen  that  this  table  is  of 
great  importance  in  studying  the  general  motions  and  pressures 
of  the  atmosphere  on  different  parallels  of  latitude  and  at  dif- 
ferent altitudes,  and  also  their  annual  changes  with  the  seasons 
of  the  year,  although  the  results  are  to  be  regarded  as  being 
only  approximate,  and,  near  the  equator,  not  at  all  accurate. 


SURFACE  WINDS,  CALMS,  AND  CALM  BELTS. 

100.  So  far  we  have  considered  mostly  the  general  circula- 
tion of  the  great  mass  of  the  atmosphere  generally,  and  deter- 
mined the  effect  of  this  in  connection  with  the  deflecting  forces 
of  the  earth's  rotation,  upon  the  atmospheric  pressures.  We 
•come  now  to  consider  the  reflex  and  secondary  action  of  this 
modified  pressure  in  modifying  the  general  circulation  arising 
•directly  from  the  temperature  gradients  between  the  equator 
and  the  poles  and  the  deflecting  forces.  It  has  been  shown, 
•§  93,  that  in  this  modified  pressure  there  is  a  zone  of  high  pres- 
sure in  each  hemisphere,  with  its  maximum  pressure  near  the 
parallel  of  30°,  and  extending  all  around  the  globe.  The  effect 
of  this  is  to  cause  the  air  at  the  earth's  surface  to  flow  out  from 
beneath,  on  the  one  hand  toward  the  equator,  and  on  the  other 
toward  the  pole.  In  the  former  case  the  flow  of  air  at  the  sur- 
face, combining  with  the  general  flow  in  the  lower  strata  from 
the  pole  toward  the  equator,  and  acted  upon  by  the  deflecting 
force  of  the  earth's  rotation,  adds  greatly  to  the  strength  of  the 
trade-winds.  In  the  latter  case,  the  flow  being  in  a  direction 
contrary  to  that  of  the  general  flow  of  the  lower  strata  from 
the  pole  toward  the  equator,  and  being  also  a  little  stronger  at 
and  near  the  earth's  surface,  there  is  a  residual  motion  toward 
the  pole  in  the  middle  latitudes,  which,  also  acted  upon  by  the 
deflecting  force  of  the  earth's  rotation,  inclines  toward  the  east, 
and  gives  rise  to  the  gentle  southwest  winds  in  the  northern 
and  northwest  winds  in  the  southern  hemisphere  in  these  lati- 
tudes. 

It  must  be  borne  in  mind  in  this  connection  that  we  are  not 
here  considering  the  actual  circulation  and  other  conditions  of 


ISO   THE    GENERAL    CIRCULATION   OF   THE   ATMOSPHERE. 

the  atmosphere  as  disturbed  from  various  abnormal  causes,  but 
the  case  of  an  earth  with  a  homogeneous  surface,  and  with 
uniform  temperatures  at  all  longitudes  on  the  same  latitudes. 
To  the  results  here  obtained  must  still  be  added  those  depend- 
ing upon  the  irregular  and  abnormal  disturbances  in  order  to 
get  the  true  results  as  observed. 

The  effect  of  these  zones  of  high  pressure,  with  their  maxi- 
ma in  the  lower  part  of  the  atmosphere  nearer  the  equator  as  the 
altitude  is  increased,  is  undoubtedly  felt  to  a  considerable  alti- 
tude, but  mostly  near  the  earth's  surface.  Above,  where  there 
is  little  friction,  the  equatorial  and  polar  motions  arising  from 
pressure  gradients,  however  produced,  we  have  seen  give  rise 
to  east  or  west  components  of  motion  which,  by  means  of  the 
deflecting  forces  of  the  earth's  rotation,  almost  entirely  coun- 
teract the  effect  of  the  pressure  gradients,  and  leave  the  veloci- 
ties of  the  polar  and  equatorial  motions  very  small  in  compari- 
son with  what  they  otherwise  would  be,  except  very  near  the 
equator,  where  the  deflecting  forces  are  very  small.  But  near 
the  earth's  surface,  where  the  friction  is  great,  it  requires 
greater  polar  and  equatorial  components  of  motion  to  overcome 
the  friction  and  to  keep  up  east  and  west  components  of  velocity 
which,  by  means  of  the  deflecting  forces  arising  from  them,, 
would  materially  interfere  with  the  free  outflow  below.  Besides,, 
since  this  outflow  of  air  below  from  beneath  the  high  pressure 
is  confined  mostly  to  a  comparatively  thin  stratum  at  the 
earth's  surface,  there  is  great  resistance  to  this  flow  both  from 
friction  between  it  and  the  earth's  surface  and  from  the  strata 
above,  which  have  much  less  motion,  and  this  in  a  somewhat 
different  direction,  since  the  motion  above  is  more  nearly  in  an 
east  or  west  direction.  It  is  therefore  necessary  to  have  com- 
paratively small  east  or  west  components  of  velocity,  so  as  to- 
leave  nearly  the  full  force  of  the  pressure  gradient  to  overcome 
the  resistance  to  the  polar  and  equatorial  motions  near  the 
earth's  surface.  For  two  reasons,  therefore,  it  is  necessary 
here,  and  wherever  there  is  much  friction,  that  the  polar  and 
equatorial  components  of  motion  shall  be  large  in  comparison 
with  the  east  and  west  ones.  While  therefore  the  motions  o£ 


SURFACE    WINDS,   CALMS,  AND   CALM-BELTS.  !$! 

the  air  are  nearly  in  a  direction  either  east  or  west  on  each  side 
of  the  zone  of  high  pressure  at  a  small  elevation  above  the 
earth's  surface,  at  and  near  the  surface  they  deviate  consider- 
ably from  these  directions,  and  assume  more  nearly  polar  and 
equatorial  directions.  Looking  at  the  matter  in  a  more  general 
way,  all  the  conditions  of  the  general  atmospheric  circulation, 
in  the  case  of  no  friction,  are  satisfied  with  east  and  west  mo- 
tions only  ;  for  the  initial  motions  may  be  such  that  the  deflect- 
ing forces  of  these  motions  exactly  counteract  the  forces  aris- 
ing from  the  temperature  and  pressure  gradients.  But  the 
greater  the  friction  and  the  less  the  deflecting  forces  of  the 
earth's  rotation,  the  greater  must  be  the  equatorial  and  polar 
motions  in  comparison  with  the  others,  and  the  greater  the 
deviation  of  the  resultant  from  an  east  or  west  direction.  As 
the  deflecting  force  of  the  earth's  rotation  becomes  small  on 
the  trade-wind  parallels,  the  trade-winds  have  a  smaller  west 
component  of  motion  than  they  otherwise  would  have  in  com- 
parison with  the  other  component. 

101.  It  is  probable  that  the  polar  motion  of  the  lower  part 
of  the  atmosphere  in  the  middle  latitudes  does  not  extend,  so 
as  to  be  sensible,  beyond  about  the  parallel  of  60°  in  either 
hemisphere.  In  the  northern  hemisphere  there  are  too  many 
abnormal  disturbances  for  the  determination  of  this  limit.  In 
the  southern  hemisphere,  on  account  of  the  smooth-water  sur- 
face in  the  middle  and  polar  latitudes,  there  are  fewer  disturb- 
ances of  this  sort ;  but  here  there  is  a  great  deficiency  of  obser- 
vations :  the  few,  however,  which  have  been  made  indicate  that 
in  the  polar  region  south  of  the  parallel  of  60°  or  65°  there  is  an 
equatorial  component  of  motion.  With  regard  to  the  winds  of 
this  region  Coffin  says  :19 

"  Of  the  third  system,  comprising  the  southern  polar  winds,  our 
knowledge  is  confined  to  the  months  of  winter  and  early  spring  (of  the 
northern  hemisphere).  Of  the  five  resultants  near  the  margin  of  the 
zone,  60°  to  65°,  all  are  from  nearly  a  south  point.  Of  the  whole  fifteen 
within  the  zone  only  five  tend  toward,  and  two  of  them  but  slightly  so, 
while  ten  recede  from  it,  generally  at  a  large  angle." 

It   seems,  therefore,    that    in    the    polar    regions    of    this 


152    THE    GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

hemisphere  the  winds,  upon  the  whole,  have  a  component  of 
motion  from  the  pole. 

102.  It  has  been  shown,  §  78,  that  the  east  component  of 
velocity  of  the  air  at  the  earth's  surface  in  the  middle  and 
polar  latitudes  depends  upon  the  rapidity  of  the  vertical  circu- 
lation and  the  relative  motions  of  the  strata  with  reference  to 
one  another  at  different  altitudes.  But  these  relative  motions, 
or  differences  of  motion  of  different  strata,  depend  upon  the 
deflecting  forces  of  the  earth's  rotation ;  and  where  these  forces 
are  very  weak,  they  do  not  nearly  come  up  to  the  limit  given 
by  the  expression  of  v  in  §  77,  which  gives  the  limit  beyond 
which  the  value  of  V—VQ  cannot  go,  and  consequently  to  the 
relative  velocities  between  the  strata  having  an  east  component 
of  velocity  ^0  at  the  earth's  surface,  and  v  at  any  altitude  h. 

The  forces  deflecting  towards  the  east  or  west  depend  upon 
the  horizontal  polar  or  equatorial  velocity,  as  is  seen  from  the 
expression  of  Fu ,  §  49.  But  very  near  the  poles  the  value  of  u 
nearly  vanishes,  since  the  interchanging  motion  of  any  particle 
of  air  between  the  equatorial  and  polar  regions  is  oscillatory, 
having  its  greatest  velocity  in  the  middle  latitudes,  which  grad- 
ually decreases  both  toward  the  equator  and  the  poles,  and 
nearly  vanishes  just  before  it  arrives  at  its  greatest  limit  of 
range.  Near  the  po^e,  therefore,  there  is  not  much  difference 
between  the  east  components  of  velocity  of  the  upper  and 
lower  strata,  and  consequently  little  force  to  overcome  the 
friction  at  the  earth's  surface  and  keep  up  an  east  component 
of  velocity  there.  Since,  therefore,  this  component  of  velocity 
in  the  polar  regions  is  small,  and  also  the  component  of  motion 
from  the  poles,  these  must  be  regions  in  which  there  is  very 
nearly  a  calm,  unless  there  is  some  abnormal  disturbance. 

At  and  near  the  equator  the  deflecting  forces  which  cause 
a  difference  in  the  east  and  west  components  of  velocity  at 
different  altitudes  vanish,  or  nearly  so,  for  two  reasons :  the 
one,  because  as  near  the  pole,  and  for  the  same  reason,  there  is 
little  motion  either  toward  or  from  the  equator ;  and  the  other, 
because  the  deflecting  forces  here,  with  any  given  velocity  u  of 
motion  toward  or  from  the  equator,  decrease  as  sin  /  de- 


SURFACE   WINDS,   CALMS,  AND   CALM-BELTS.  1 53 

^creases,  and  entirely  vanishes  at  the  equator.  The  relative 
velocities  between  the  strata,  therefore,  vanish  at,  and  are  very 
small  near,  the  equator ;  and  consequently  the  same  is  the  case 
with  the  force  which  overcomes  the  friction  at  the  earth's  sur- 
face and  maintains  an  east  or  west  component  of  motion  there. 
And  as  there  is  no  motion  north  or  south  between  the  systems 
of  winds  of  the  two  hemispheres  where  the  trade-winds  meet, 
which  is  near  the  equator,  there  is  here  a  belt  of  calms  extending 
around  the  globe,  where  not  interfered  with  by  abnormal  dis- 
turbances or  forces  not  considered  in  the  general  circulation  of 
the  atmosphere. 

103.  For  reasons  given  in  §  80  there  can  be  no  east  or  west 
'Component  of  motion  at  the  earth's  surface  on  the  parallel  of 
maximum  atmospheric  pressure  on  the  earth's  surface,  at  or 
near  the  parallel  of  30°.  And  as  the  air  is  pressed  out  at  the 
-earth's  surface,  toward  the  pole  on  the  one  side  and  the  equa- 
tor on  the  other,  from  beneath  the  zone  of  high  pressure,  there 
is  no  sensible  motion  north  or  south  in  the  middle  part  of  this 
.zone.  There  is  then  here,  in  each  hemisphere,  a  belt  of  calms, 
extending  around  the  globe,  and  having  its  middle  on  this  par- 
allel of  latitude,  except  so  far  as  it  is  interfered  with  by  abnor- 
mal disturbances  not  here  considered. 

Since  the  deflecting  forces  arising  from  the  much  greater 
east  components  of  velocity  in  the  southern  hemisphere,  both 
at  the  earth's  surface  and  at  all  altitudes,  are  much  stronger 
than  the  similar  and  opposing  forces  of  the  northern  hemi- 
sphere, the  southern  system  of  circulation  encroaches  some- 
what upon  the  area  of  the  other,  causing  all  the  calm-belts  to 
be  a  little  further  north  than  they  otherwise  would  be,  so  that 
the  equatorial  calm-belt  is  a  little  north  of  the  equator,  while 
the  tropical  calm-belt  of  the  northern  hemisphere  is  a  little  fur- 
ther from  the  equator  than  that  of  the  southern  hemisphere. 
For  the  same  reason  there  is,  on  the  average  of  the  year,  a  lit- 
tle more  air  in  the  northern  than  in  the  southern  hemisphere, 
as  may  be  seen  from  an  inspection  of  the  barometric  pressures 
in  the  second  column  of  the  table  of  §  95,  although  the  maxi- 
mum about  the  parallel  of  30°  in  the  southern  hemisphere  is  a 


154  THE   GENERAL    CIRCULATION  OF   THE  ATMOSPHERE. 

little  greater  than  that  of  the  northern,  on  account  of  a  little 
greater  bulging  up  of  the  isobaric  surfaces. 

SUMMARY  AND   GRAPHIC   REPRESENTATION   OF  THE   MOTIONS 
AND   PRESSURES. 

104.  In  the  preceding  part  of  this  chapter  it  has  been  shown 
that  if  all  parts  of  the  atmosphere  had  the  same  temperature 
there  would  be  a  complete  calm  over  all  parts  of  the  earth's 
surface.  But  that  in  consequence  of  the  difference  of  temper- 
ature between  the  equatorial  and  polar  regions  of  the  globe, 
and  the  consequent  temperature  gradient,  there  arise  pressure 
gradients  and  forces  which  give  rise  to  and  maintain  a  vertical, 
circulation  of  the  atmosphere  with  a  motion  of  the  air  of  the 
upper  strata  of  the  atmosphere  from  the  equator  toward  the 
poles,  and  a  counter  current  in  the  lower  part  from  the  poles 
toward  the  equator,  as  represented  by  the  arrows  in  the  follow- 
ing figure,  and  that  this  of  course  requires  a  gradual  settling 
down  of  the  air  from  the  higher  to  the  lower  strata  in  the  mid- 
dle and  higher  latitudes,  and  the  reverse  in  the  lower  latitudes. 
It  has  also  been  shown  that  in  case  the  earth  had  no  rotation 
on  its  axis,  this  would  be  exclusively  a  vertical  circulation  in 
the  planes  of  the  meridians  without  any  east  or  west  compo- 
nents of  motion  in  any  part ;  but  that,  in  consequence  of  the 
deflecting  forces  arising  from  the  earth's  rotation,  the  atmos- 
phere at  the  earth's  surface  has  also  an  east  component  of  mo- 
tion in  the  middle  and  higher  latitudes,  and  the  reverse  in  the 
lower  latitudes,  and  that  the  velocities  of  the  east  components 
increase  with  increase  of  elevation,  so  that  at  great  altitudes 
they  become  very  much  greater  than  those  at  the  earth's  sur- 
face ;  wjiile  those  of  the  west  components  decrease  with  in- 
crease of  altitude  up  to  a  certain  altitude,  where  they  vanish 
and  change  signs  and  become  east  velocities,  now  increasing 
with  increase  of  altitude  to  the  top  of  the  atmosphere. 

It  has  been  further  shown  that  the  deflecting  forces  arising 
from  the  cast  components  of  motion  of  each  hemisphere  from 
the  earth's  surface  to  the  top  of  the  atmosphere,  in  the  middle 


SUMMARY  OF   THE   MOTIONS  AND  PRESSURES. 


and  higher  latitudes  and  of  the  upper  part  of  the  atmosphere 
in  the  lower  latitudes,  drives  the  atmosphere  from  the  polar 
regions  toward  the  equator,  while  those  arising  from  the  west- 
components  of  motion  in  the  lower  part  of  the  atmosphere  in 
the  lower  latitudes,  having  a  contrary  effect,  but  small  in  com- 
parison with  the  other  on  account  of  the  weakness  of  these 
forces  near  the  equator,  tend  to  drive  the  air  a  little  from  the 
equator  toward  the  poles.  There  is,  therefore,  a  depression  of 
the  isobaric  surfaces  at  all  altitudes  in  the  polar  regions,  espe- 
cially in  the  southern  hemisphere,  a  much  smaller  depression- 
in  the  equatorial  regions,  and  a  bulging  up  of  the  isobaric  sur- 
faces in  the  vicinity  of  the  parallel  of  30°  in  the  lower  part  of 
the  atmosphere,  the  maximum  being  nearer  the  equator  as  the- 
altitude  increases,  as  represented  in  Fig.  4,  but  at  high  altitudes. 
there  is  a  minimum  of  barometric  pressure  at  the  poles  and  a. 
maximum  at  the  equator. 


In  the  accompanying  figure  the  solid  arrows  in  the  interior 
part  represent  the  resultant  motions  of  the  winds  (longer  ar- 


1156   THE    GENERAL    CIRCULATION-  OF    THE    ATMOSPHERE. 

rows  indicating  greater  velocities),  in  case  of  an  earth  with  a 
homogeneous  surface  over  both  hemispheres,  in  which  the  mo- 
tions would  be  symmetrical  in  both  and  the  same  at  all  longi- 
tudes, and  the  equatorial  and  tropical  calm-belts  would  be  situ- 
ated at  equal  distances  from  each  pole.  The  dotted  arrows 
indicate  the  strong,  almost  eastern  motion  of  the  air  at  all  lati- 
tudes at  some  high  altitude,  as  that  of  the  cirrus  clouds. 

The  outline  of  the  outer  part  of  the  figure  represents  an 
isobaric  surface  high  up  where  the  bulging  up  near  the  parallel 
•of  30°  disappears  and  the  maximum  pressure  at  the  same  alti- 
tude is  transferred  to  the  equator.  For  lower  altitudes  the 
.isobaric  surfaces  have  a  bulging  up  at  the  parallel  of  30°,  and 
•a  slight  depression  at  and  near  the  equator.  The  arrows  in  this 
part  represent  the  polar  and  equatorial  components  of  motion, 
the  former  above  and  the  latter  below,  except  near  the  earth's 
.surface  on  the  polar  sides  of  the  tropical  calm-belts,  where 
there  is  a  polar  component  of  motion  arising  from  the  air's  be- 
ing pressed  out  from  under  the  belt  of  high  pressure.  This, 
perhaps,  does  not  extend  beyond  the  polar  circles,  beyond 
which  there  can  be  little  motion  in  any  direction,  except  from 
abnormal  disturbances. 

For  reasons  given  in  §  103,  the  actual  mean  positions  of  the 
equatorial  and  tropical  calm-belts  are  not  precisely  as  here  rep- 
resented, but  are  all  a  little  displaced  toward  the  north  pole, 
and  the  polar  depression  of  the  isobaric  surfaces  is  greater  in 
the  southern  than  in  the  northern  hemisphere. 

ANNUAL  OSCILLATION   OF   THE   CALM-BELTS. 

105.  For  the  same  reason  that  there  is  a  semi-annual  inver- 
sion of  the  interchanging  motions  between  the  two  hemispheres, 
in  the  one  direction  in  the  spring  and  the  contrary  in  the  fall, 
from  which  results  an  annual  inequality  of  the  atmospheric 
pressure  at  the  earth's  surface,  §  94,  there  is  also  an  annual 
oscillation  of  the  calm-belts.  During  the  summer  of  the  north- 
ern hemisphere,  while  there  is  a  flow  of  air  below  from  the 


ANNUAL    OSCILLATION  OF    THE    CALM-BELTS.  l$f 

southern  to  the  northern  hemisphere  and  the  contrary  above, 
the  vertical  circulation  and  interchanging  motion  of  the  south- 
ern hemisphere,  due  to  the  difference  of  the  mean  temperatures 
of  the  equatorial  and  polar  regions,  is  strengthened  while  that 
of  the  northern  hemisphere  is  weakened.  The  consequence  is 
that  the  southern  stronger  system  at  this  season  encroaches 
somewhat  upon  the  territory  of  the  other,  causing  the  middle 
of  the  equatorial  calm-belt,  which  is  the  dividing  line  between 
the  two  systems,  to  be  a  little  north  of  its  mean  position ;  and 
as  the  tropical  calm-belts  are  intermediate  between  the  equa- 
torial calnrubelt  and  the  poles,  and  their  positions  must  depend 
somewhat  upon  the  extension  and  the  limits  of  the  systems, 
respectively  to  which  they  belong,  the  positions  of  these  also 
must  be  thrown  further  north,  when  that  of  the  equatorial  calm- 
belt  is.  Of  course  just  the  reverse  takes  place  during  the 
winter  of  the  northern  hemisphere.  There  is,  therefore,  an 
annual  oscillation  of  all  the  calm-belts,  such  that  they  have 
their  most  northerly  position  in  midsummer  and  the  reverse  in 
midwinter  of  the  northern  hemisphere. 

Or  looking  at  the  matter  in  a  somewhat  different  way,  we 
have  seen  that  the  southern  system  of  circulation,  for  the  mean 
of  the  year,  especially  the  east  components  of  motions,  due  to 
the  same  temperature  gradients,  or  nearly,  between  the  equator 
and  the  poles  as  in  the  northern  hemisphere,  is  stronger  than 
that  of  the  northern  one  on  account  of  there  being  less  frictional 
resistance  at  the  earth's  surface  to  the  former  than  to  the  latter, 
and  that  in  consequence  of  this  the  mean  position  of  the  equa- 
torial calm-belt  is  a  little  north  of  the  equator  and  both  the 
tropical  calm-belts  are  a  little  farther  north  than  they  otherwise 
would  be,  and  so  at  unequal  distances  from  the  equator.  Now 
the  effect  is  the  same  whether  we  diminish  the  resistance  or 
increase  the  forces.  In  the  summer  season,  therefore,  of  the 
northern  hemisphere,  when  the  forces  are  increased  in  the 
southern  and  diminished  in  the  northern  hemisphere,  we  have 
exactly  the  same  effect  as  where  the  resistances  are  less  in 
the  southern  and  greater  in  the  northern  hemisphere,  namely,. 


158   THE    GENERAL    CIRCULATION  OF   THE   ATMOSPHERE. 

that  all  the  calm-belts  are  thrown  a  little  to  the  north  of  their 
>mean  positions,  or  positions  which  they  otherwise  would  have ; 
and  the  reverse  in  the  winter  season  of  the  northern  hemi- 
sphere. 

106.  Since  the  equatorial  calm-belt  depends  upon  two 
•circumstances,  the  meeting  below  of  the  air  currents  belonging 
to  the  two  hemispherical  systems  of  circulation,  and  the  vanish- 
ing of  the  forces  which  cause  a  westerly  motion  of  the  air,  its 
northern  limit  is  better  defined  than  the  equatorial  or  southern 
limit,  and  its  range  of  oscillation  is  greater.  In  the  summer 
reason  of  the  northern  hemisphere,  when  the  lower  currents  of 
the  two  system  meet  at  a  greater  distance  north  of  the  equator, 
the  forces  on  the  north  side  of  the  belt  which  gives  rise  to  the 
west  component  of  motion  are  very  much  stronger  than  those 
on  the  equatorial  side  very  near  the  equator,  where  these  forces 
almost  entirely  vanish.  Over  the  whole  space  therefore  be- 
tween the  calm-belt  and  the  equator  these  forces  sensibly  vanish, 
so  that,  although  the  southeast  trade-winds  blow  beyond  the 
equator,  yet  they  have  here,  and  for  a  few  degrees  north  of  the 
equator,  no  west  component  of  motion,  and  become  southerly 
winds,  and  of  little  strength  on  account  of  their  being  so  near 
the  place  of  meeting  where  all  motion  ceases.  The  winds,  then, 
between  the  equator  and  the  calm-belt  are  weak,  especially  at 
the  season  when  this  belt  is  near  the  equator,  so  that  the 
southern  limit  of  the  belt  is  then  uncertain,  and  the  southeast 
trade-winds  appear  to  vanish  soon  after  passing  the  equator, 
and  even  when  the  belt  has  its  most  northerly  position  these 
winds  are  too  weak  to  be  observed  far  beyond  the  equator. 
There  is,  therefore,  an  apparent  widening  of  the  calm-belt  dur- 
ing the  summer  season  of  the  northern  hemisphere. 

107.  The  preceding  theoretical  deductions  with  regard  to 
the  calm-belts  are  fully  confirmed  by  observations  of  the  trade 
winds  in  both  the  great  oceans  of  both  hemispheres. 

The  following  table  of  the  northern  limits,  in  different  longi- 
tudes, of  the  northeast  trade-wind  in  the  Atlantic  Ocean  was 
given  by  Maury : l3 


ANNUAL   OSCILLATION  OF    THE    CALM-BELTS. 


59 


LONGITUDE  AAr  . 

LATITUDE  OF  COMMENCEMENT  OF  N.E.  TRADES  IN  — 

Winter. 

Spring. 

Summer. 

Autumn. 

70° 

28° 

28°.  7 

29°  -3 

29°.  o 

65 

26.3 

28   .0 

29  -3 

28   .3 

60 

24 

24  -3 

27  -3 

28  .3 

55 

22 

22   .7 

24  -7 

25   .0 

50 

21 

23    -7 

28  .3 

23  .7 

45 

23 

24  -7 

31  -3 

28    .7 

40 

27.7 

29  -7 

30  -7 

29  -3 

35 

26 

27  -3 

30  .7 

25   -7 

30 

24-3 

28  .7 

29  -7 

26  .7 

25 

25-3 

24  .7 

3i  -3 

26  .3 

20 

24-3 

28.3 

28  .7 

27   .0 

15 

29 

31  .0 

32  .0 

3i   -3 

10 



31  -3 

34  -7 

32  .0 

The  following  tables  were  prepared  by  Woeikoff  from  the 
"  Pilot  *Chart  of  the  Atlantic  Ocean,"  edited  by  the  Meteoro- 
logical Office  in  London  : 20 

MEAN   POLAR   LIMITS   OF  THE  N.E.   TRADE-WIND. 


MONTHS. 

MERIDIANS  WEST. 

65 

60 

55 

50 

45 

40 

35 

30 

25 

20 

17 

Jan.  to  Mar.. 
Apr.  to  June. 
July  to  Sept. 
Oct.  to  Dec.  . 

26° 
28.5 
27 
26 

25° 

24.5 
27 
24 

23°-  5 

23 

26    .5 

22    .5 

23° 
25 
26 
22 

24°  -5 
27 

26  .5 

22    .5 

20° 
28 
27-5 
24-5 

26°.  5 

28 
27    -5 
25    -5 

25°.  5 
28 
28   .5 

25   -5 

25°.  5 
28   .5 
3i 
26  .5 

28°.  5 
32 
31   -5 
29  -5 

30° 
33 
32-5 
3i 

MEAN   POLAR   LIMITS   OF  THE   S.E.   TRADE-WIND. 


MERIDIANS. 


30  w. 

25  W. 

20  W. 

15  W. 

10  W. 

sw. 

o 

SB. 

10  E. 

15  E. 

Jan.  to  March  
-April  to  June 

19°  -5 
2=      c 

21° 

21 

24° 
24 

26°.  5 

2^ 

28° 
25 

29° 

27 

30° 

28   5 

3i°.  5 

•32 

32°.  5 

•7-7       e 

33° 

July  to  Sept  

20     <; 

22.  5 

24 

24  .5 

27.  5 

28.5 

2Q.  5 

2Q    .  5 

-JQ    .  *> 

Oct   to  Dec 

16     * 

18  s 

20  ^ 

21 

22    5 

28 

28    5 

2Q 

VQ 

l6o  THE   GENERAL    CIRCULATION   OF   THE  ATMOSPHERE. 


EQUATORIAL     LIMITS     OF    THE     NORTHERN     AND     SOUTHERN: 

TRADE-WINDS. 


MONTHS. 

MERIDIANS  WEST. 

40 

35 

3° 

25 

20 

*7 

(  N.  E  .. 

3°      N. 
i        N. 
1.5    N. 
i        S. 
3-*    N. 
0.5    S. 
8.5    N. 
4        N. 
11.5    N. 
6        N. 
6        N. 
4-5    N. 

i°-5  N. 

o  .sN. 
o 
o  -5S. 

3  N. 
o 

9  N. 
4  N. 

12           N. 

4  N. 
6  N. 
4  N. 

2°      N. 

i      N. 
o.sN. 
i      S. 
3-5  N. 

2        N. 

10      N. 
3      N. 
ii.  5N. 

2        N. 

6      N. 
3-5N. 

4°-  5  N. 

2           N. 

2   .sN. 
o  .5  N. 
5   -5N. 

3        N. 

12           N. 

3        N. 
ii        N. 

2           N. 

6        N. 
3   -5N. 

6°.  5  N. 

3        N. 
5        N. 
o.sN. 
8   .s  N. 
3   -5N. 
14        N. 
3        N. 

12           N. 

o        N. 
9  -5N. 
4        N. 

8°  N. 
3    N. 
6    N. 
i    N. 

Jan.      ]s    E 

,      N   E  .. 

March|s  E...  :..::.. 

(  N   E 

May      ]s    E 

IN.  E  

Ju]y    \  s  E     

(  N   E... 

Sept.   {£•£• 

{  N   E    . 

NOV.   If;!; 

108.  The  first  of  the  last  three  tables  does  not  diffSr  more 
from  the  preceding  one,  given  by  Maury,  than  is  to  be  expected 
in  determining  a  limit  so  ill-defined  as  that  of  the  northern  limit 
of  the  northeast  trade-wind,  which  is  likewise  the  southern  limit 
of  the  northern  tropical  calm-belt.  Either  of  these  tables  indi- 
cates that  there  is  an  annual  oscillation  of  this  limit  with  a 
range  of  about  three  degrees  of  latitude,  and  having  its  most 
northerly  position  in  midsummer.  It  is  seen,  also,  that  this 
limit  does  not  coincide  with  any  parallel  of  latitude  across  the 
Atlantic  Ocean,  but  it  has  a  more  northerly  position  on  each 
side  of  the  ocean  than  in  the  middle,  the  longitude  of  minimum 
latitude  being  that  of  about  50°  W. 

There  are  observations  that  indicate  that  the  northern  limit 
of  this  tropical  calm-belt  has  a  corresponding  oscillation.  When 
this  belt  in  the  fall  moves  southward  from  its  most  northerly 
position,  it  has  been  observed  that  the  southwest  winds  are  felt 
first  on  the  coast  of  Portugal,  then  at  Madeira,  and  afterwards, 
at  Teneriffe  and  the  Canaries. 

The  southern  limit  of  the  southeast  trade-wind  is  not  so  well 
determined  from  observation ;  but  according  to  the  second  of 
the  last  three  tables,  this  wind  extends  to  about  the  same  dis- 
tance from  the  equator  as  the  northeast  trade-wind,  and  it  has. 


ANNUAL   OSCILLATION  OF   THE   CALM-BELTS.  l6l 

also  an  annual  oscillation  corresponding  to  that  of  the  northern 
limit  of  the  northeast  trade-wind,  having  its  most  northerly 
position  about  the  same  time,  as  required  by  theory,  but  this 
oscillation  is  not  so  marked,  the  range  being  smaller.  In  this 
case  the  limit  lies  nearest  the  equator  on  the  west  side  of  the 
ocean,  and  is  about  ten  degrees  further  towards  the  south  on 
the  other  side. 

According  to  the  last  of  the  preceding  tables,  the  equato- 
rial limit  of  the  northeast  trade-wind,  which  is  likewise  the 
northern  limit  of  the  equatorial  calm-belt,  has  a  range  of  annual 
oscillation  of  about  twelve  degrees  of  latitude,  from  20°  to  40° 
W.  longitude,  with  a  position,  at  all  seasons,  a  little  more 
northerly  on  the  east  than  on  the  west  side  of  the  field  of  obser- 
vation, the  extreme  northerly  position  here  in  summer  being 
about  the  parallel  of  13°  N.  But  the  equatorial  limit  of  the 
southeast  trade-wind,  which  is  also  the  southern  limit  of  the 
equatorial  calm-belt,  has  a  much  smaller  range,  for  reasons 
given  in  §  102,  it  being  only  about  five  degrees  on  the  west  side 
on  the  longitude  of  40°  W.,  and  sensibly  vanishing  on  the  east 
side  of  the  ocean.  The  most  southerly  position,  in  March,  is 
about  one  degree  south  of  the  equator. 

Since  the  northern  limit  of  the  equatorial  calm-belt  has  a 
much  greater  range  of  oscillation  than  the  southern  limit, 
especially  on  the  east  side,  it  follows  that  this  calm-belt  is  much 
wider  in  summer  than  in  winter,  and  especially  so  on  the  eastern 
side  of  the  ocean. 

109.  Kerhallet,  according  to  Dove,13  gave  the  following 
table  of  the  extent  of  the  trade-winds  in  the  Pacific  Ocean, 
compiled  from  the  observations  of  92  ships  : 

The  irregularity  in  these  numbers  indicates  that  they  are 
not  very  accurate;  but  still  they  plainly  show,  as  in  the  Atlantic 
Ocean,  that  the  limits  of  both  the  northeast  and  southeast 
trade-winds  have  an  oscillatory  movement  with  a  range,  in  the 
equatorial  limits  at  least,  of  several  degrees  of  latitude,  and 
that  the  mean  position  of  the  equatorial  calm-belt  lies  north  of 
the  equator,  and  has  a  greater  width  in  summer  than  in  winter. 
This  greater  width  here,  as  in  the  Atlantic  Ocean,  it  is  seen 


1 62    THE    GENERAL    CIRCULATION  OF   THE   ATMOSPHERE. 
CONSIDERATIONS   GENERALES   SUR  L'OCEAN  PACIFIQUE,  1856. 


MONTH. 

POLAR  LIMIT. 

EQUATORIAL  LIMIT. 

Breadth 
of 
Calm-belt. 

N.E.  Trade, 
Lat.  N. 

S.E.  Trade, 
Lat.  S. 

N.E.  Trade, 
Lat.  N. 

S.E.  Trade, 
Lat.  N. 

21°     0' 
28    28 
29     o 
30     o 
25     5 
27   4i 
3i    43 
29   30 
24   20 
26     6 

25      9 
24     o 

33°  25' 
28    51 
31    10 
27   25 
28    24 
25     o 

25  28 

24    18 
24   5i 
23    27 
28   39 

22     30 

6°  30' 

4      I 
8    15 
4  45 
7    52 
9   58 
12     5 
15     o 
13    56 

12     20 

5°    o' 

2       0 

5    50 

2       O 

3    36 

2     30 

5     4 

2     30 

8    n 
3   32 

1*56 

3°  30 

2       I 
*    2    25 

2   45 
4    16 
7    28 

7      i 
12    30 

5   45 
8   48 

3*  16 

February             

March      

April    

May   

Jung        ,  

Tulv  .  . 

August               •  • 

September  

October  

November               .  .    . 

December       

5    12 

from  the  table,  is  due  to  the  greater  range  of  oscillation  of  the 
northern  than  of  the  southern  limit  of  the  belt. 

We  are  not  advised  with  regard  to  the  part  of  the  ocean 
where  the  observations  were  mostly  made,  so  that  it  is  uncer- 
tain whether  these  results  are  applicable  to  the  belt  generally 
in  this  ocean,  and  whether  the  mean  positions  of  the  limits  and 
the  range  of  oscillation  may  not  differ  considerably  at  different 
longitudes. 

It  had  formerly  been  supposed  that  the  mean  position  of 
these  limits  and  of  the  central  parts  of  the  calm-belts  in  this 
ocean  were  nearly  symmetrically  situated  with  regard  to  the 
two  hemispheres,  the  central  line  of  the  equatorial  calm  coin- 
ciding with  the  equator.  Kaemtz  places  the  limits  of  the  north- 
east trade-wind  at  23°  and  2°  N.,  and  those  of  the  southeast 
trade-wind  at  21°  and  2°  S.  But  the  equatorial  calm-belt  in 
this  ocean,  as  in  the  Atlantic  Ocean,  doubtless  lies  a  little  north 
of  the  equator. 


CHAPTER  IV. 
•CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION. 

ON  THE   RELATIVE  CLIMATES  OF  THE  LOWER  AND 
HIGHER   LATITUDES. 

110.  IN  consequence  of  the  interchange  of  equatorial  and 
polar  waters,  especially  in  the  southern  hemisphere,  as  ex- 
plained in  §  68,  the  equatorial  regions  of  the  globe  are  colder, 
and  the  polar  regions  warmer,  than  they  otherwise  would  be. 
A  similar,  but  perhaps  a  much  smaller,  effect  is  produced  by 
the  interchange  of  the  warm  air  of  the  equatorial,  and  the  cold 
-air  of  the  polar,  regions  in  the  general  circulation  of  the  atmos- 
phere. Although  the  volume  of  air  interchanged  in  a  given 
time  is  much  greater  than  that  of  the  water  of  the  ocean,  yet 
the  mass  is  probably  less,  since  the  mass  of  the  whole  atmos- 
phere is  only  equal  to  that  of  an  ocean  covering  the  whole  sur- 
face of  the  earth  of  about  10  meters  in  depth,  and  as  the 
.specific  heat  of  air  is  only  0.2375,  the  whole  capacity  of  the 
atmosphere  for  heat  is  only  equal  to  that  of  an  ocean  of  2.5 
meters  in  depth.  If  we  suppose  the  ocean  to  have  a  uniform 
depth  of  5000  meters  (3. 1  miles),  the  interchanging  velocity  in 
the  case  of  the  atmosphere  would  have  to  be  2000  times  as 
great  as  that  of  the  ocean  to  give  rise  to  an  equal  transfer  of 
heat  from  the  equatorial  to  the  polar  regions.  The  velocity  of 
interchange  in  the  case  of  the  atmosphere  is,  of  course,  much 
the  greater ;  but  it  can  scarcely  be  regarded  as  being  2000  times 
as  great  as  that  of  the  ocean,  for  it  must  be  remembered  that 
the  motion  of  the  atmosphere,  except  at  the  earth's  surface, 
•and  at  all  altitudes  near  the  equator,  is  mostly  easterly  or 
westerly,  the  polar  and  equatorial  components  of  motion  being 
generally  small  in  comparison  with  the  east  and  west  com- 
ponents. It  is  probable,  therefore,  that  the  amount  of  heat 

163 


164  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION. 

transferred  from  the  equatorial  to  the  polar  regions  is  less  in' 
the  case  of  the  atmosphere  than  in  that  of  the  ocean.  But  we 
have  reason  to  think  that  the  difference  of  temperature  be- 
tween the  equator  and  the  polls  is  very  much  diminished  by 
the  latter,  and  therefore  the  effect  of  the  former  in  the  same 
direction  must  be  at  least  quite  sensible. 

The  relation  between  the  hygrometric  states  of  the  atmos- 
phere of  the  lower  and  higher  latitudes  is  also  affected  by  the 
general  vertical  circulation.  In  the  middle  and  higher  latitudes- 
there  is  a  gradual  settling  down  of  the  atmosphere  toward  the 
earth's  surface,  where  the  temperature  is  higher  than  it  is  above  ; 
and  so  here  the  relative  humidity  gradually  becomes  less,  and 
being  very  small  above  it  becomes  still  much  less  after  having, 
descended  to  the  lower  strata.  In  the  lower  latitudes,  and. 
especially  near  the  equator,  on  the  contrary,  where  there  is  a 
gradual  ascent  of  the  air  from  the  lower  strata,  where  the  tem- 
perature is  much  greater,  to  the  upper  ones,  where  it  is  much, 
less,  the  relative  humidity  is  gradually  increased,  even,  it  may- 
be, to  complete  saturation.  Of  course  the  absolute  amount  of 
vapor  in  the  higher  latitudes,  on  account  of  the  lowness  of 
temperature,  is  much  less  than  in  the  lower  latitudes,  but  if 
there  was  the  same  relative  humidity  in  both,  the  effect  of  the 
vertical  circulation  would  be  to  decrease  that  of  the  higher 
latitudes  and  to  increase  that  of  the  lower  latitudes. 

WET  AND   DRY   ZONES. 

111.  As  all  the  vapor  of  evaporation,  or  nearly,  over  both 
trade-wind  zones  of  about  20°  in  width,  especially  where  the 
trade-winds  are  regular,  as  on  the  ocean,  is  carried  into  the 
comparatively  narrow  zone  of  the  equatorial  calm-belt  before  it 
ascends  to  sufficient  height  to  be  condensed  into  rain,  the 
amount  of  rain  falling  in  this  belt  is  very  large  and  the  cloud 
nearly  continuous.  The  equatorial  calm-belt,  therefore,  is  also 
a  cloud-  and  rain-belt.  The  height  to  which  the  vapor  of  the 
surface  currents  ascends  before  condensation  and  cloud-forma- 
tion take  place  depends  upon  the  amount  of  moisture  in  the- 


W 'ET  AND   DRY  ZONES.  165 

.air  at  the  earth's  surface,  and  so  upon  the  difference  between 
the  air  temperature  and  that  of  the  dew-point.  The  height  at 
'which  condensation  commences  is  given  accurately  by  Table 
IV,  and  is  nearly,  under  all  conditions,  125  meters  for  each 
•degree  Centigrade  of  the  depression  of  the  dew-point  below  the 
,air  temperature,  as  explained  in  §  27. 

The  first  vapor  condensed  is  supported  and  carried  farther 
up  by  the  ascending  current  in  the  form  of  cloud  and  small 
particles  of  rain,  and  the  more  the  stronger  the  current  is. 
Small  particles  are  carried  upward  by  the  current,  and  the  still 
smaller  ones  more  rapidly  than  the  larger  ones,  and  so  the  dif- 
ferent sizes  of  the  smaller  drops,  being  carried  up  with  different 
velocities,  come  in  contact  and  combine  until  they  form  drops 
too  large  to  be  supported  by  the  ascending  current,  and  these 
then  fall  as  rain.  The  stronger  the  ascending  current  the 
larger  the  drops.  When  there  is  no  ascending  current  there  is 
no  rain,  though  there  may  be  fog  and  mist. 

The  daily  amount  of  evaporation  on  the  ocean  within  the 
tropics  is  about  one  fourth  of  an  inch  per  day.  If  then  all  this 
amount  of  vapor  over  zones  say  1000  miles  in  width  on  each 
side 'is  carried  into  the  calm-belt  say  300  miles  in  width,  and  is 
there  condensed  and  falls  as  rain,  then  the  daily  rainfall  is  1.67 
inches  per  day ;  and  if  this  belt  were  to  remain  stationary  >  it 
would  be,  for  the  average  of  the  width,  about  60  feet  per  year. 
But  since  the  cloud-  and  rain-belt,  as  the  calm-belt,  oscillates 
through  a  range  generally  more  than  twice  as  great  as  its  width, 
this  amount  of  rain  is  distributed,  in  the  course  of  the  year, 
over  a  zone  more  than  three  times  as  wide,  and  hence,  in  gen- 
eral, less  than  one  third  of  this  amount  falls  in  any  one  place 
during  the  year. 

The  calm-belt,  as  it  exists  at  any  given  time,  is  mostly  nar- 
rower than  the  belt  on  which  rain  falls  ;  for  as  the  air  in  the 
•equatorial  region  generally,  but  mostly  over  the  surface  calm- 
belt,  ascends  it  gradually  expands  and  diverges  from  the  cen- 
tral line  of  this  belt  to  form  the  upper  return  current  toward 
the  poles ;  and  before  the  vapor  is  all  condensed,  and  while  the 
air  is  still  ascending,  it  is  carried  out  beyond  the  limits  of  the 


1 66  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION.. 

calm-belt,  so  that   considerable  rain  falls  at  some  distance  be- 
yond these  limits. 

Of  course  neither  the  calm-belt  nor  the  rain-  and  cloud-belt 
has  very  definite  limits,  but  these  are  much  better  defined  over 
the  great  oceans,  where  the  trade-winds  blow  very  steadily  in 
nearly  the  same  direction  and  with  the  same  force,  than  on  the 
continents,  where  regularity  of  outline  is  very  much  interfered 
with  by  the  various  abnormal  disturbances  of  uneven  surfaces, 
and  mountain  ranges,  and  likewise  by  the  monsoons  of  the 
Indian  Ocean  and  others.  The  rain-belt  is,  however,  clearly 
traceable  across  the  whole  of  Africa,  wherever  observations 
have  been  made,  as  also  across  the  American  isthmus,  but  it 
has  greater  width,  and  its  limits  are  not  so  well  defined.  The 
zone  on  which  rain  falls  during  the  course  of  the  year  has  been 
given  on  a  chart  by  WoeikofL21  This,  on  the  great  oceans,, 
lies  mostly  between  i°  and  11°  north  latitude  ;  but  on  the  west 
coast  of  Africa  it  extends  a  little  farther  north,  and  on  the  east 
coast  of  South  America  to  about  5°  south  latitude.  These 
limits  correspond  pretty  closely  with  the  extreme  northern 
limit  of  the  southeast  trade-wind  in  January  on  the  one  hand, 
and  the  extreme  southern  limit  of  the  northeast  trade-wind  in 
July  on  the  other,  as  given  in  the  tables  of  §  107  and  §  109  ; 
and  so  the  rainy  zone  falls  nearly  within  the  range  of  oscillation 
of  the  calm-belt. 

112.  Loomis"  has  given  a  chart  of  mean  annual  rainfall  on 
which  the  northern  limit  of  the  zone  of  50  inches  and  upward 
of  mean  annual  rainfall,  on  the  continent  of  Africa,  lies  mostly 
between  the  parallels  of  10°  and  12°  north  latitude,  but  the 
southern  limit  is  more  irregular  and  extends  from  a  point  near 
the  equator  on  the  west  coast  to  about  10°  south  on  the  east 
coast  of  Africa.  Beyond  these  limits,  both  north  and  south,, 
there  is  a  gradual  shading  off  on  the  chart  and  diminution  in 
the  amount  of  rainfall,  so  that  although  the  rainy  zone  here 
has  no  definite  limits,  yet  the  amount  of  rain  falling  a  little 
north  of  the  equator,  on  the  parallels  of  latitude  corresponding 
to  those  of  the  rain-belt  on  the  oceans,  as  the  result  of  the  gen- 
eral circulation  of  the  atmosphere  and  meeting  near  the  equa- 


WET  AND  DRY  ZONES. 

tor  of  the  vapor-laden  surface  currents  of  the  trade-winds  is 
unusually  great,  notwithstanding  the  amount  of  evaporation 
over  the  land  surface  is  much  less  than  on  the  ocean,  and  this 
vapor,  on  account  of  the  inequalities  of  the  land  surface  and 
the  frictional  resistances,  is  not  all  carried  so  nearly  into  the 
central  line  of  the  meeting  of  the  trade-winds  as  on  the  smooth 
ocean  surface. 

Farther  east,  over  the  islands  of  Sumatra,  Java,  Borneo,  and 
Celebes,  and  also  over  the  Malayan  peninsula,  all  lying  on  and 
near  the  equator,  the  mean  annual  rainfall,  according  to  the 
chart,  is  still  more  abundant  ;  for  they  all  fall  within  the  zone 
of  75  inches  and  over  of  rainfall,  and  at  many  individual  sta- 
tions the  annual  rainfall  is  over  150  inches,  and  even  more 
than  200  inches  at  Buitenzorg,  Java,  all  going  to  show  the  ten- 
dency to  a  concentration  of  rainfall  in  a  zone  at  and  near  the 
equator.  The  amount  of  rainfall  here  is  much  greater  than 
over  the  continent  of  Africa,  because  the  amount  of  evapora- 
tion over  the  warm  ocean  surface  is  greater ;  but  on  account  of 
the  monsoon  influences,  to  be  considered  hereafter,  this  rain- 
fall is  scattered  over  a  much  wider  zone  than  on  the  ocean 
generally,  and  consequently  the  rainfall  in  the  central  parts  of 
the  rainy  zone  is  less,  and  the  zone  has  no  definite  limits. 

In  the  northern  part  of  South  America,  a  little  north  of  the 
equator,  this  chart  does  not  indicate  that  there  is  a  distinct  and 
well-defined  rainy  zone,  as  on  the  same  parallels  on  the  two 
great  oceans,  because  it  is  mostly  obscured  by  the  rainfalls  over 
a  great  part  of  South  and  Central  America,  arising  from  the 
influence  of  the  mountain  chain  of  the  Andes,  to  be  explained 
farther  on.  There  is  much  evidence,  however,  to  show  that 
here  also  there  is,  at  least  in  many  places,  a  distinct  rain-belt, 
oscillating  with  the  seasons,  and  having,  at  any  given  time, 
definite  limits  beyond  which  little  or  no  rain  falls. 

The  latent  heat  given  out  in  the  condensation  of  the  great 
amount  of  aqueous  vapor  carried  into,  and  ascending  in,  the 
calm-belt  gives  additional  strength  to  the  trade-winds.  In  con- 
sequence of  this  heat  the  upper  part  of  the  air,  above  the  plane 
of  incipient  condensation,  is  not  cooled  by  expansion  down  to 


1 68  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION. 

the  temperature  of  the  air  on  each  side,  and  hence  the  tendency 
to  ascend  in  this  belt  is  very  much  stronger  than  that  of  the 
air  on  each  side,  which  simply  ascends  with  sufficient  rapidity 
to  supply  the  returning  polar  currents  above,  in  the  general 
vertical  interchange  between  the  equatorial  and  polar  regions, 
which,  we  have  seen,  is  small,  the  force  arising  from  the  differ- 
ence of  temperature  between  the  equator  and  the  poles  being 
almost  entirely  counteracted  by  the  deflecting  forces  arising 
from  the  earth's  rotation.  Hence  there  is  a  very  rapid  ascent 
of  air  in  this  belt,  which  requires  an  increased  equatorial  com- 
ponent of  velocity  in  the  trade-winds  near  the  earth's  surface  to 
supply  it,  and  this  adds  greatly  to  their  strength.  This  is  en- 
tirely a  secondary  matter,  dependent  upon  the  general  vertical 
circulation,  for  if  it  were  not  for  this  the  air,  with  its  aqueous 
vapor,  would  not  ascend  at  all,  and  hence  no  condensation 
would  take  place. 

113.  The  air  within  the  rain-belt  being  almost  entirely 
calm,  and  also  warm  and  nearly  saturated  with  vapor,  is  always 
extremely  oppressive,  such  as  is  sometimes  experienced  for  a 
short  time  in  other  regions  of  the  globe  when  the  air  is  warm 
and  calm,  and  saturated,  or  nearly  so,  with  aqueous  vapor.  A 
graphic  description  of  the  kind  of  weather  which  is  usually  ex- 
perienced under  the  cloud-ring  of  the  equatorial  calm-belt  is 
found,  as  cited  by  Maury,23  in  the  journal  of  Commodore  Sin- 
clair, kept  on  board  of  the  United  States  frigate  Congress  dur- 
ing a  cruise  to  South  America  in  1817-18.  He  crossed  it  in  the 
month  of  January,  1818,  between  the  parallel  of  4°  north  and 
the  equator,  and  between  the  meridians  of  19°  and  23°  west. 
He  says  of  it : 

"This  is  certainly  one  of  the  most  unpleasant  regions  on  our  globe. 
A  dense,  close  atmosphere,  except  for  a  few  hours  after  a  thunder-storm, 
during  which  time  torrents  of  rain  fall,  when  the  air  becomes  a  little 
refreshed  ;  but  a  hot,  glowing  sun  soon  heats  it  again,  and  but  for  your 
awnings,  and  the  little  air  put  in  circulation  by  the  continual  flapping  of 
the  ship's  sails,  it  would  be  almost  insufferable.  No  person  who  has  not 
crossed  the  region  can  form  an  adequate  idea  of  its  unpleasant  effects. 
You  feel  a  degree  of  lassitude  unconquerable,  which  not  even  sea-bathing, 
which  everywhere  else  proves  so  salutary  and  renovating,  can  dispel. 


WET  AND  DRY  ZONES.  169 

Except  when  in  actual  danger  of  shipwreck,  I  never  spent  twelve  more 
disagreeable  days  in  the  professional  part  of  my  life  than  in  these  calm 
latitudes. 

"  I  crossed  the  line  on  the  I7th  of  January, at  eight  A.M.,  in  longitude 
21°  20',  and  soon  found  I  had  surmounted  all  the  difficulties  consequent 
to  that  event ;  that  the  breeze  continued  to  freshen  and  draw  around  to 
the  south-southeast,  bringing  with  it  a  clear  sky  and  most  heavenly 
temperature,  renovating  and  refreshing  beyond  description.  Nothing 
was  now  to  be  seen  but  cheerful  countenances,  exchanging  as  by 
•enchantment  from  that  sleepy  sluggishness  which  had  borne  us  all  down 
lor  the  last  two  weeks." 

But  notwithstanding  the  oppressive  character  of  the  weather 
under  the  cloud-ring  the  temperature  is  not  extremely  high — 
much  less  so  than  on  either  side  of  it,  and  the  disagreeable 
-and  oppressive  character  arises  mostly  from  the  calmness  and 
extreme  dampness  of  the  air.  The  great  cloud-ring  protects 
the  earth's  surface  from  the  almost  vertical  rays  of  the  sun, 
.and  hence  it  is  considerably  cooler  than  on  either  side  where 
the  sun's  heat  reaches  the  earth's  surface  unobstructed.  Espy 
found  from  examining  the  tables  of  Wilkes  that  in  the  rainy 
belt  of  the  equator  the  temperature  of  the  air  on  the  ocean  is 
about  6°  F.  lower  than  it  is  beyond  the  borders  of  the  rains 
.both  north  and  south.  On  land  the  difference  is  much  greater. 
According  to  Humboldt,  each  side  of  the  belt  of  rains  in  South 
America  is  from  10°  to  18°  hotter  than  in  the  belt  of  rains. 
This  is  caused,  not  only  by  the  absence  of  the  heating  rays  of 
the  sun  in  the  rain-belt,  but  also  by  the  cooling  effect  of  the 
drops  of  rain  coming  down  from  high  and  cold  altitudes. 

114.  From  the  general  circulation  of  the  atmosphere  and 
meeting  of  the  trade-winds  near  the  equator,  and  the  annual 
oscillation  and  shifting  of  the  parallels  on  which  they  meet,  arise 
peculiarities  of  climate  within  the  zone  of  the  range  of  oscilla- 
tion of  the  calm-  and  rain-belt,  such  as  are  not  to  be  found  else- 
where. Since  the  calm-belt  with  its  daily  torrents  of  rain  oscil- 
lates forth  and  back  annually  through  a  range,  especially  on  the 
great  oceans,  more  than  twice  as  great  as  its  width,  while  just 
outside  of  the  limits  of  this  narrow  belt,  with  winds  from  dif- 
ferent directions  on  the  two  sides,  there  is  no  rainfall  at  the 


170  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION.. 

time,  this  is  necessarily  a  zone  of  alternations  of  extremely  wet: 
and  extremely  dry  seasons,  and  of  winds  which  vary  in  direction 
at  different  seasons  of  the  year.  The  position  of  a  place  with, 
regard  to  the  mean  position  of  the  oscillating  rain-belt  may  be 
such  that  there  is  either  a  long  rainy  and  a  long  dry  season' 
during  the  year,  or  two  rainy  seasons  of  shorter  duration  with 
two  intervening  dry  seasons.  The  latter  takes  place  where  the 
station  is  situated  at  or  near  the  mean  position  of  the  middle 
of  the  rain-belt,  and  the  range  of  oscillation  is  considerably 
greater  than  the  width  of  the  belt,  as  it  generally  is,  on  the 
oceans ;  for  then  the  middle  of  the  belt,  as  it  moves  towards- 
the  north,  is  over  the  place  of  observation  in  April  or  May,  and 
again  in  October  and  November  as  it  moves  back  southward, 
and  at  these  times  there  is  a  great  abundance  of  rain.  But  in 
July  or  August,  when  the  rain-belt  has  its  most  northerly  posi- 
tion and  its  southern  limit  is  north  of  the  place,  or  in  January 
or  February,  when  it  has  its  most  southerly  position,  and  its 
northern  limit  is  south  of  the  place,  there  is  of  course  no  rain- 
fall. There  are,  consequently,  in  this  case,  two  wet  and  two 
very  dry  seasons  in  the  course  of  the  year.  Or  the  width  of 
the  rain-belt  and  the  range  of  oscillation,  especially  on  land, 
may  be  such  that  there  is  no  total  cessation  of  rain  during  the 
year,  but  simply  two  minima  instead  of  the  two  dry  seasons, 
and  so  two  maxima,  one  in  the  middle  of  each  of  the  rainy  sea- 
sons. 

If  the  place  of  observation  is  a  little  north  of  the  mean  posi- 
tion of  the  rain-belt,  so  that  its  southern  limit  never  moves 
north  of  the  place,  then  there  is  no  intervening  dry  season  when 
the  belt  has  its  extreme  northerly  position,  though  there  may 
be  a  considerable  diminution  in  the  rate  of  rainfall  in  August  or 
September,  when  a  minimum  only  occurs  instead  of  a  complete 
cessation  and  a  very  dry  season,  but  a  long  drought  at  the 
opposite  season  of  the  year.  On  the  other  hand,  if  the  place  is 
so  far  south  of  the  mean  position  of  the  oscillating  rain-belt 
that  the  northern  limit  of  the  belt,  in  its  extreme  southerly 
position,  does  not  lie  beyond  it,  then  there  is  no  complete  ces- 
sation of  rain  in  January  or  February,  but  simply  a  minimum 


WET  AND  DRY  ZONES.  I?l 

in  the  monthly  rainfalls,  preceded  and  followed  by  a  maximum,, 
while  at  the  opposite  season  of  the  year  there  may  be  no  rain 
for  several  months.  The  position  of  the  place  also  and  the 
width  of  the  rain-belt  may  be  such  as  to  cause  a  rainy  season 
without  a  minimum  in  the  middle,  and  in  such  cases  the  dry 
season  is  much  longer  than  the  rainy  season. 

Since  on  the  north  side  of  the  rain-belt  the  winds  are  gener- 
ally from  some  point  between  north  and  east,  and  in  the  other 
from  some  point  between  south  and  east,  wherever  the  rain-belt,, 
in  its  annual  oscillations,  passes  entirely  over  a  place,  there  is  a 
change  of  the  winds  from  some  point  in  the  northeast  to  one  in 
the  southeast  quadrant,  or  the  contrary,  Since  the  calm-belt 
is  sometimes  considerably  north  of  the  equator,  the  southeast 
trade-winds,  after  passing  the  equator,  in  consequence  of  the 
influence  of  the  earth's  rotation,  then  become  southerly  or  even 
southwesterly  winds  near  the  southern  border  of  the  calm-belt. 

115.  The  preceding  deductions  from  theoretical  considera- 
tions are  verified  by  numerous  observations  of  the  monthly 
rainfalls  and  prevailing  directions  of  the  wind  at  many  places 
near  the  equator,  all  around  the  globe.  Since  the  oscillating 
calm,  and  the  accompanying  rain-belt  always  follow  each  other 
and  occupy  the  same  parallels,  except  that  the  latter  is  a  little 
the  wider,  the  oscillations  of  the  calm-belt  can  be  more  readily 
traced  from  the  observations  of  the  monthly  rainfalls  than  from 
the  direct  observations  of  the  winds  and  calms. 

The  following  table  of  average  monthly  rainfalls  on  the 
Congo  and  the  southwest  coast  of  Africa  has  been  taken  from 
a  work  by  Dr.  A.  v.  Danckelman." 

At  Vivi,  5°  40'  S.,  13°  49'  E.,  it  is  seen  that  there  is  a  total 
cessation  of  rain  during  June,  July,  and  August,  and  very  near- 
ly so  in  September,  while  at  the  opposite  season  of  the  year 
there  is  only  a  minimum  with  a  maximum  preceding  in  Novem- 
ber and  one  following  in  April.  The  station  being  south  of  the 
equator,  during  the  summer  of  the  northern  hemisphere,  when 
the  rain-belt  has  its  most  northerly  position,  the  southern  bor- 
der of  this  belt  was  entirely  north  of  the  place,  notwithstand- 
ing it  is  wider  at  this  land  station  than  on  the  ocean  and  its, 

o 


:-I72  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION. 


MONTH. 

MONTHLY  RAINFALLS  IN  MILLIMETERS  AT 

Vivi. 

Ponta  da 
Lenha. 

Gabun. 

Chinchoxo. 

Loanda. 

96 
68 
103 
231 
50 

0 

o 
o 

I 
75 
237 
1  80 

65 
104 

94 
118 

27 

0 

o 
o 

T 

3 
143 

53 

155 
217 
349 
381 
169 

7 
i 
ii 
40 
288 

423 
224 

311 
1  2O 

185 
IO2 

54 

0 

o 

5 
8 

23 

222 

52 

39 
30 

58 

122 

12 
O 
0 

I 
2 

4 

51 

25 

JFebruary       .      ...    .  .    ... 

March     

April   

May  

Tune             

July   .                                

August                       .       ... 

September     .    .... 

November           

December     

Year  

1,041 

608 

2,265 

1,082 

344 

limits  not  so  well  defined,  and  so  no  rain  fell  for  several  months. 
The  minimum  in  February,  if  there  are  no  abnormal  local  dis- 
turbances, indicates  the  middle  of  the  rain-belt  at  this  time  is 
.south  of  the  station,  and  if  so,  it  must  have  a  more  southerly 
mean  position  or  a  wider  range  than  on  the  Atlantic  Ocean. 
What  has  been  stated  here  with  regard  to  Vivi  is  also  true  of 
, Ponta  da  Lenha. 

At  Gabun,  o°  30'  N.,  9°  35'  E.,  since  it  lies  farther  north,  the 
rainfall  does  not  quite  vanish  in  the  summer  of  the  northern 
hemisphere,  and  the  minimum  of  the  opposite  season  is  less 
marked  than  at  Vivi.  The  same  is  true  with  renard  to  Chin- 
choxo, except  that  here  there  seems  to  be  a  total  cessation  of 
rain  during  June  and  July,  but  the  numbers  expressing  the 
monthly  rainfalls  seem  to  be  very  irregular,  and  so  are  perhaps 
not  very  reliable. 

At  Loanda,  8°  49'  S.,  13°  f  E.,  there  is  much  less  rain  than 
at  Vivi ;  but  there  are  two  maxima  and  two  minima,  with  an 
intervening  minimum  in  the  winter  of  the  northern  hemisphere 
and  a  total  cessation  of  rain  for  several  months  at  the  opposite 
.season  of  the  year,  as  at  Vivi. 

At  the  island  of  St.  Thomas,  o°  20'  N.,  6°  43'  E.,  and  so  of 
.nearly  the  same  latitude  as  Gabun,  from  the  average  of  five  or 


WET  AND  DRY  ZONES.  173', 

six  years  of  observation,  no  rain  fell  in  July ;  in  June,  July,, 
August,  and  September  only  47  mm.  of  rain  fell ;  while  the 
amount  for  the  whole  year  on  the  average  was  1019  mm.  The 
greatest  amount  fell  in  March.36 

116.  "In  Nango,  13°  N.,  9°  W.,  from  Paris,  the  rainy  season  com- 
mences the  latter  part  of  May,  but  the  rain  is  then  only  seldom.  It  be- 
comes more  frequent  in  July.  The  rainfall  then  is  very  great.  The- 
temperature  then  sinks  still  more.  The  rain  holds  on  in  August,  and  is 
as  abundant  as  in  July.  The  temperature  is  then  a  minimum.  Septem- 
ber brings  a  great  change,  but  the  rain  is  still  frequent.  The  temperature- 
rises  again,  and  the  air  becomes  more  clear."  26 

This  place,  being  9°  north  of  the  equator,  is  within  the  rain- 
belt  from  June  to  September  inclusive,  and  the  rainfall  during 
the  middle  part  of  this  period  is  abundant ;  but  during  the 
other  eight  months  of  the  year,  when  the  rain-belt  has  moved 
southward,  the  northern  limit  of  the  belt  is  south  of  the  place, 
and  hence  there  is  no  rain. 

Observations  on  the  upper  Nile  in  the  interior  of  Africa, 
both  of  the  winds  and  the  rainfall,  indicate  clearly  the  exist- 
ence of  the  calm-  and  rain-belt  there.  At  Rubaga,  o°  20'  N.,  32^ 
45'  E.,  altitude  1300  meters,  the  mean  probability  of  rain  is  as 
follows : 

Jan.       Feb.       Mar.       April.       May.       June.      July      Aug.       Sept.       Oct.       Nov.       Dec. 
43  42  42  ?o  51  60  29  46  52  74  67  47 

There  are,  therefore,  two  maxima  and  two  minima,  as  usual 
at  places  near  the  equator ;  but  the  numbers  indicate  that  the 
rain-belt  here  is  wide  and  not  well  defined,  and  so,  instead  of 
two  rainy  and  two  dry  seasons,  there  are  simply  two  maxima 
and  two  minima  of  rainfall. 

At  Lado,  5°  2'  N.,  31°  50'  E.,  the  winds  from  April  to  Sep- 
tember are  mostly  from  S.W.  and  S. ;  from  October  to  March, 
N.  and  N.E.  The  greatest  rainfall  is  in  August  and  Septem- 
ber ;  the  least  in  December,  January,  and  February." 

These  observations,  as  well  as  those  of  Rubaga,  indicate 
that  the  calm-  and  rain-belt  here  is  but  little  north  of  the 
equator,  and  that  its  width  and  range  of  oscillation  are  such 
that  the  places  are  at  all  times  comprised  between  its  limits  ; 


174  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION. 

tout  since  there  is  more  rain  during  the  summer  than  the  win- 
ter of  the  northern  hemisphere,  the  mean  position  of  the  mid- 
>dle  of  the  belt  must  be  south  of  Lado.  The  winds,  however, 
indicate  that  the  mean  position  cannot  be  far  from  Lado. 

"  At  Nyassa  Sea  (south  of  the  equator)  there  is  no  rain  between  May 
-and  October.  The  soil  becomes  dried  out,  and  the  grass  becomes  dry 
-and  assumes  the  appearance  of  wheat-fields  in  England  in  July." 

During  this  dry  season  the  rain-belt  is  north  of  the  equator, 
.and  Nyassa  Sea  is  left  in  the  zone  of  the  southeast  trade-winds, 
where  there  is  no  rain. 

During  Emin  Effendi's  travels  in  equatorial  Africa,  from 
Nov.  29  to  Dec.  1 8,  1877,  from  Mreili,  3°  N.,  to  Rubaga 
(Mtesa's  residence),  rain  fell  nearly  every  day  in  great  abun- 
dance, and  the  whole  country  was  flooded  with  water,  and  the 
travellers  had  to  wade  through  water  often  from  two  to  three 
feet  deep." 

The  middle  line  of  the  rain-belt,  therefore,  at  this  time, 
which  is  about  the  time  of  its  mean  position,  must  have  been 
.about  two  degrees  north  of  the  equator. 

117.  In  the  northern  part  of  South  America  and  the 
Isthmus  of  Panama  the  middle  line  of  the  rain-belt  seems  to 
oscillate  between  the  equator  and  the  parallel  of  10°  or  12° 
N, ;  and  so,  in  its  mean  position,  is  considerably  north  of  the 
equator. 

At  Guatemala,  14°  38'  N.,9O°  31'  W.;  altitude  1480  m.,  from 
three  years  of  observations,  1880-1882,  the  average  monthly 
rainfall  in  millimeters  is: 

Jan.     Feb.      Mar.     April.     May.      June.     July.     Aug.     Sept.      Oct.     Nov.     Dec.     Year. 
4  6  i  20  144         253          137         234         231         159         51  2  1242 

Hence  this  place  is  fully  within  the  limits  of  the  rain-belt  from 
May  to  November,  but  during  the  rest  of  the  year,  while  the 
belt  has  a  more  southerly  position,  it  is  almost  wholly  north  of 
the  northern  limit  of  the  belt,  where  it  receives  little  or  no  rain. 
"There  is  an  indication  of  a  slight  minimum  in  July  also,  from 
which  it  seems  that  the  middle  of  the  rain-belt  passes  a  little 
north  of  Guatemala  at  this  time. 


WET  AND  DRY  ZONES.  1/5 

At  Greytown,  Nicaragua,  lat.  10°  55'  N.,  according  to  Com- 
mander A.  V.  Reed,  "  the  dry  season  lasts  till  late  in  May, 
when  the  rains  set  in  and  are  of  daily  occurrence  during  June 
and  July,  with  considerable  thunder  and  lightning.  In  August 
and  September,  they  have  very  pleasant  weather,  with  less  rain, 
and  the  sea  outside  is  usually  smooth  ;  but  in  October  and  No- 
vember again  they  have  disagreeable  weather  and  daily  rains." 

Here  again,  it  seems,  there  are  two  maxima,  one  in  June  or 
July  and  the  other  in  October  or  November,  with  a  minimum 
in  August  or  September,  and  a  long  dry  season  at  the  opposite 
season  of  the  year.  This  indicates  that  the  mean  position  of 
the  middle  of  the  rain-belt  is  considerably  south  of  Greytown ; 
for  at  any  place  in  the  middle  of  the  belt  in  its  mean  position 
the  two  maxima  would  occur  at  exactly  opposite  times  of  the 
year,  and  there  would  be  two  intervening  dry  seasons  of  equal 
length,  in  which  there  would  probably  be  one  or  two  months 
with  scarcely  any  rain. 

From  the  report  of  Lieut.  Frederick  Collins  of  the  survey 
for  an  Interoceanic  Canal  in  the  State  of  Cauca,  we  learn  that, 
at  the  junction  of  the  Napipi  and  Merindo  rivers  (about  5° 
N.),  "  as  a  rule,  two  well-marked  dry  seasons  are  experienced 
here,  with  corresponding  periods  of  rain.  January,  February, 
and  March  are  the  months  which  constitute  the  dryest  and 
pleasantest  season.  In  April  the  rains  commence,  and  in  May 
and  June  they  are  very  heavy.  In  July  a  second  dry  season 
begins  to  set  in,  and  August  and  September  are  generally 
pleasant  and  comparatively  dry.  In  October  rains  again  com- 
mence, and  in  November  and  December  they  are  the  heaviest." 

Here  the  mean  position  of  the  middle  of  the  rain-belt  seems 
to  be  a  little  south  of  the  place,  since  the  dry  season  of  August 
and  September  is  not  so  marked  and  of  as  long  duration  as 
that  of  January,  February,  and  March. 

On  the  Panama  Interoceanic  Ship  Canal,  8°. 5  N.,  "the  year 
is  divided,  as  in  other  parts  of  the  American  isthmus  and  of 
Central  America,  into  two  seasons,  the  rainy  and  the  dry,  the 
former  beginning  in  the  latter  part  of  May  and  lasting  until 
November,  when  it  gives  place  to  the  latter,  which  lasts  until 


1/6  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION.. 

May  comes  around  again.  The  annual  rainfall  is  from  90  to 
1 40  inches."28 

This  place  being  a  little  farther  north  than  the  preceding 
one,  there  are  here  only  a  wet  and  a  dry  season,  the  former 
taking  place  while  the  belt  is  north  of  its  mean  position  ;  but, 
as  in  other  places  considerably  north  of  the  equator,  if  we  had 
the  monthly  rainfalls,  a  minimum  in  August  or  September 
would  undoubtedly  be  observable. 

The  effect  of  the  oscillation  of  the  rain-belt  near  the  equator 
in  producing  a  wet  and  a  dry  season  seems  to  be  felt  in  Mexico. 
Humboldt  says : 

"  There  are  only  two  seasons  known  in  the  equatorial  region  of  Mex- 
ico, even  as  far  as  the  28th  degree  of  N.  latitude :  the  rainy  season,  esta- 
cion  de  las  aguas,  which  begins  in  the  month  of  June  or  July,  and  ends 
in  the  month  of  September  or  October ;  and  the  dry  season,  el  estio, 
which  lasts  eight  months,  from  October  to  the  end  of  May."  29 

118.  Although  the  rain  falls  every  day  in  the  rain-belt  dur- 
ing at  least  the  middle  part  of  the  rainy  season,  yet  it  is  not 
continuous  through  both  the  day  and  night,  but  it  takes  place 
mostly  during  the  day.  The  abundant  downpour  of  rain,  at 
least  on  land,  seems  to  be  of  the  nature  of  thunder  showers  in 
all  countries  during  very  warm  and  damp  weather,  and  to  de- 
pend upon  the  heating  effects  of  the  sun's  rays  in  inducing  a 
state  of  unstable  equilibrium,  so  that  the  aqueous  vapor  brought 
in  by  the  trade-winds  into  the  calm-belt  ascend  and  are  con- 
densed into  rain,  mostly  while  the  atmosphere  is  in  this  state. 
Tomlinson  says : 30 

"The  atmospheric  phenomena  of  such  countries  as  lie  under  the  calm- 
belt  are  marked  by  a  striking  uniformity  and  regularity.  For  hours  after 
the  rising  of  the  sun  the  sky  remains  entirely  free  from  clouds.  About 
noon  a  few  clouds  appear  at  the  horizon,  which,  as  they  become  more 
vertical,  rapidly  increase  in  size  and  density;  presently  the  thunder  is- 
heard,  the  wind  blows  in  violent  gusts,  and  at  the  same  time  there  occurs 
a  heavy  downpour  of  rain,  which  lasts  for  a  few  hours.  The  clouds 
•  quickly  disappear  toward  evening,  and  the  sun  sets  in  a  deep-blue  and 
cloudless  sky.  It  is  rare  for  rain  to  fall  during  more  than  eight  hours  at 
a  time.  The  countries  near  the  equator  experience  this  kind  of  weather 
nearly  all  the  year,  and  what  is  called  the  rainy  season  differs  from  the 


WET  AND   DRY  ZONES. 

remainder  of  the  year  in  the  rain  being  rather  more  continuous  and 

plentiful." 

This,  or  at  least  the  latter  part,  seems  to  apply  more  espe- 
cially to  continents  where  the  rainfall  is  more  scattering  and  not 
well  defined,  and  not  to  the  ocean,  or  even  to  the  American 
isthmus,  where,  we  have  seen,  there  are  long  seasons  with  little 
or  no  rain. 

Since  the  origination  of  the  shower  or  daily  rainfall  de- 
pends upon  the  unstable  state,  which  is  more  readily  induced 
during  the  heat  of  the  day,  the  rain  commences  at  that  time ; 
but  after  an  abundant  fall  of  rain  for  several  hours,  some  of 
which  descends  from  very  high  altitudes  where  the  air  and  the 
condensed  vapor  are  very  cold,  the  unstable  state  of  the  atmos- 
phere toward  evening  is  destroyed  by  the  cooling  effect  of  the 
rain  upon  the  lower  strata  of  the  atmosphere,  and  the  rain 
ceases  until  next  day,  when  the  unstable  state  is  again  induced. 

119.  The  following  contrasts  of  the  wet  and  the  dry  sea- 
sons on  the  Orinoco  and  the  great  Amazonian  basin  within 
the  range  of  oscillation  of  the  rain-belt,  and  which  is  true  of  all 
places  within  this  range  where  the  rain-belt  is  narrow  and  well 
defined,  and  not  much  affected  by  the  abnormal  disturbances, 
but  is  somewhat  as  it  is  on  the  ocean  and  on  level  countries 
near  the  ocean,  have  been  given,  as  cited  by  Maury,23  by  Hum- 
boldt  in  his  "Aspects  of  Nature:" 

"  When,  under  the  vertical  rays  of  the  never-clouded  sun,  the  carbon- 
ized turfy  covering  falls  into  dust,  the  indurated  soil  cracks  asunder  as  if 
from  the  shock  of  an  earthquake.  If  at  such  times  two  opposing  cur- 
rents of  air,  whose  conflict  produces  a  rotary  motion,  come  in  contact 
with  the  soil,  the  plain  assumes  a  strange  and  singular  aspect.  Like 
conical-shaped  clouds,  the  points  of  which  descend  to  the  earth,  the  sand 
rises  through  the  rarefied  air  on  the  electrically  charged  centre  of  the 
whirling  current,  resembling  the  loud  water-spout,  dreaded  by  the  ex- 
perienced mariner.  The  lowering  sky  sheds  a  dim,  almost  straw-colored 
light  on  the  desolate  plain.  The  horizon  draws  suddenly  nearer,  the 
steppe  seems  to  contract,  and  with  it  the  heart  of  the  wanderer.  The 
hot,  dusty  particles  which  fill  the  air  increase  its  ^uffocating  heat,  and 
the  east  wind,  blowing  over  the  long-heated  soil,  brings  with  it  no  re- 
freshment, but  rather  a  still  more  burning  glow.  The  pools,  which  the 


1?8  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION'. 

yellow,  fading  branches  of  the  fan-palm  had  protected  from  evaporation, 
now  gradually  disappear.  As  in  the  icy  north  the  animals  become  torpid 
with  cold,  so  here,  under  the  influence  of  the  parching  drought,  the  croc- 
odile and  the  boa  become  motionless  and  fall  asleep,  deeply  buried  in 
the  mud.  .  .  . 

"  The  distant  palm-bush,  apparently  raised  by  the  influence  of  the  con- 
tact of  unequally  heated  and  therefore  unequally  dense  strata  of  air, 
hovers  above  the  ground,  from  which  it  is  separated  by  a  narrow  inter- 
vening margin.  Half  concealed  by  the  dense  clouds  of  dust,  restless  with 
the  pain  of  thirst  and  hunger,  the  horses  and  cattle  roam  around,  the 
cattle  lowing  dismally,  and  the  horses  stretching  out  their  long  necks, 
and  snuffing  the  wind,  if  haply  a  moister  current  may  betray  the  neigh- 
borhood of  a  not  wholly  dried-up  pool.  .  .  . 

"  At  length,  after  the  long  drought,  the  welcome  season  of  the  rain 
arrives  ;  and  then  how  suddenly  is  the  scene  changed  !  .  .  . 

"  Hardly  has  the  surface  of  the  earth  received  the  refreshing  moisture 
when  the  previously  barren  steppe  begins  to  exhale  sweet  odors,  and  to 
clothe  itself  with  killingias,  the  many  panicles  of  the  paspulum,  and  a 
variety  of  grasses.  The  herbaceous  mimosas,  with  renewed  sensibility 
to  the  influence  of  light,  unfold  their  drooping,  slumbering  leaves  to 
greet  the  rising  sun;  and  the  early  song  of  birds  and  the  opening  blos- 
soms of  the  water  plants  join  to  salute  the  morning." 

120.  We  have  seen  that  under  the  high  pressure  of  the 
tropical  calm-belts  there  is  a  gradual  settling  down  of  the  air  to 
supply  the  outward  flow  on  each  side  at  the  earth's  surface 
from  beneath  this  high  pressure.  The  aqueous  vapor  in  these 
belts  cannot  rise  up  so  as  to  be  condensed,  but,  on  the  contrary, 
it  rather  sinks  down  and  is  carried  away  by  the  surface  cur- 
rents ;  on  the  one  hand,  by  the  trade-winds  to  the  equatorial 
calm-belt,  and  on  the  other,  away  toward  the  middle  latitudes. 
The  tropical  calm-belts  are  therefore  dry  belts.  Over  the 
trade-wind  latitudes,  also,  since  the  horizontal  and  compara- 
tively strong  surface  currents  hurry  away  the  vapor  which  is 
evaporated  over  the  ocean  and  the  land  surface  of  these  lati- 
tudes to  the  equatorial  calm-belt,  where  alone  it  rises  up  to 
where  it  can  be  condensed,  there  is  scarcely  any  rainfall. 
There  is,  therefore,  in  each  hemisphere,  a  wide  zone,  extending 
from  the  zone  of  equatorial  variable  rains,  over  the  trade-wind 
latitud.es  and  comprising  the  tropical  calm-belt,  in  which  there 
is  little  rain,  especially  on  the  oceans,  where  the  general  vertical 


'RELATIVE  EAST  AND    WEST   TEMPERATURES.         1/9 

•circulation  is  more  regular.  It  is  true  there  is  considerable 
rain  in  some  places  within  these  zones,  but  this  is  due  to  abnor- 
mal disturbances  of  mountain  ranges,  and  not  to  the  general 
circulation  of  the  atmosphere,  such  as  would  exist  if  the  whole 
surface  of  the  earth  were  homogeneous. 

These  zones  are  almost  completely  rainless  on  most  parts 
of  the  great  oceans,  but  there  is  at  least  a  strong  tendency 
toward  this  same  condition  on  the  continents,  as  is  readily  seen 
from  an  inspection  of  Loomis's  chart  of  Mean  Annual  Rainfall. 
In  the  northern  hemisphere  between  the  parallels  of  15°  and 
40°,  are  the  dry  regions  of  California,  Arizona,  and  Colorado  in 
North  America,  the  great  Sahara  and  Nubian  deserts  of  North 
Africa,  and  the  dry  region  of  Arabia  and  Persia  in  Asia.  In 
the  southern  hemisphere  within  the  same  parallels  are  the  dry 
regions  of  the  southern  part  of  the  Argentine  Republic  and  of 
•eastern  Patagonia  in  South  America,  a  large  dry  region  in 
South  Africa,  and  one  comprising  the  whole  of  the  interior  of 
Australia.  It  must  not  be  understood  that  these  regions  are 
entirely  rainless  throughout  the  year,  but  simply  that  the 
amount  of  rain  is  very  scant,  and  small  in  comparison  with 
that  of  the  middle  latitudes  of  each  hemisphere.  Even  in  the 
.great  Sahara  rain  sometimes  falls. 

RELATIVE  TEMPERATURES   OF  EAST  AND  WEST  SIDES  OF  THE 

CONTINENTS. 

121.  One  of  the  principal  climatic  effects  arising  from  the 
general  circulation  of  the  atmosphere  is  the  great  difference  of 
temperatures  observed  on  the  same  latitudes  on  the  east  and 
west  sides  of  the  continents,  especially  in  high  latitudes,  both 
in  the  annual  means  of  temperature  and  also  in  the  extreme 
temperatures  of  the  seasons.  It  is  a  matter  of  observation, 
which  has  been  explained  in  §  68,  that  the  mean  annual  tem- 
peratures of  the  oceans  in  the  higher  latitudes  are  greater,  and 
those  of  the  lower  latitudes  less,  than  those  of  the  same  lati- 
tudes on  the  continents  ;  and  the  differences  would  be  still 
greater  if  it  were  not  for  the  equalizing  tendency  of  the  general 


ISO  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION. 

circulation  around  the  globe,  easterly  in  the  higher,  and  the 
contrary  at  the  earth's  surface  in  the  lower,  latitudes.  The 
effect,  also,  of  this  circulation  is  to  cause  the  highest  mean 
annual  temperatures  of  the  oceans  in  the  higher  latitudes  to  be 
on  the  east  sides,  near  the  continents,  and  the  lowest  mean 
temperatures  of  the  continents  to  be  on  the  east  sides  of  the 
continents  near  to  the  adjacent  oceans.  Hence  there  are  the 
greatest  contrasts  between  the  east  sides  of  the  oceans  and  of  the 
continents.  From  a  chart  of  isotherms  for  the  mean  tempera- 
tures of  the  year  it  is  seen  that  the  mean  annual  temperature 
of  the  Atlantic  Ocean  near  the  coast  of  Norway  is  40°  F.,  while 
on  the  same  latitude  in  the  eastern  part  of  Siberia  it  is  only 
about  10°  F.  There  is  also  a  difference  of  about  20°  between 
the  mean  annual  temperatures  of  the  British  Isles  and  those  of 
the  same  latitudes  on  the  eastern  side  of  Asia.  Likewise  the 
difference  of  mean  annual  temperatures  between  the  North 
Pacific  Ocean,  adjacent  to  Alaska  in  the  neighborhood  of  the 
Aleutian  Islands,  and  those  of  corresponding  latitudes  of  Hud- 
son's Bay  and  Labrador,  is  about  15°,  but  for  latitudes  a  little 
lower,  some  less. 

Since  the  annual  inequalities  of  temperature  are  very  great 
on  the  continents  in  comparison  with  those  on  the  ocean,  the 
greatest  contrasts  of  temperature  are  found  in  the  winter  season. 
For  since  the  mean  annual  temperatures  on  the  ocean  in  the 
higher  latitudes  are  considerably  above  those  of  the  same  lati- 
tude on  the  continent,  and  the  range  of  annual  oscillation  is 
small  on  the  ocean,  the  mean  midwinter  temperatures  scarcely 
fall  to  the  mean  annual  temperatures  of  the  land  ;  and  so  the 
differences  of  the  temperatures  on  the  ocean  and  on  the  conti- 
nent, when  the  east  sides  are  compared,  are  equal  to  the  whole 
differences  between  the  annual  mean  and  the  midwinter  tem- 
peratures of  the  latter.  Thus  the  mean  temperature  of  the 
ocean  in  January  between  Iceland  and  Norway,  according  to- 
Buchan's  charts,  is  about  35°  F.,  while  that  of  eastern  Siberia  is 
—  40°,  a  difference  of  about  75°.  Between  the  mean  January 
temperatures  of  the  ocean  west  of  the  British  Isles  and  those 
of  the  same  latitudes  in  the  eastern  part  of  Asia  the  difference 

\ 


RELATIVE   EAST  AND    WEST   TEMPERATURES.         l8l 

is  less,  but  still  about  60°.  Between  the  eastern  sides  of  the 
North  Pacific  and  the  corresponding  latitudes  on  the  east  side 
•of  America  the  differences  in  January  are  nearly  as  great. 

In  midsummer  the  contrasts  in  the  higher  latitudes  made 
in  a  similar  manner  are  much  less  and  reversed,  the  oceans  at 
this  season  being  colder  than  the  continents.  But  still  there 
are  considerable  differences  when  we  compare  the  eastern  sides 
of  the  oceans  with  those  of  the  continents.  The  July  mean 
temperature  midway  between  Iceland  and  Norway  is  about  10° 
less  than  on  the  same  latitude  in  the  eastern  part  of  Asia,  and 
the  difference  between  the  Aleutian  Islands  and  Labrador  on 
the  same  latitude  is  about  the  same. 

On  the  lower  latitudes,  those  of  the  trade-winds,  the  differ- 
ences between  the  mean  annual  temperatures  of  the  continents 
and  the  oceans  are  considerable,  those  of  the  continents  being 
the  higher.  The  differences  in  midsummer  are  still  greater, 
but  in  midwinter  the  temperatures  are  somewhat  the  same. 

122.  The  characteristics  of  a  continental  climate  in  the 
-middle  and  higher  latitudes  are  great  extremes  in  the  annual 
changes  of  temperature  with  the  maxima  and  minima  occurring 
earlier  in  the  season,  a  dry  atmosphere,  and  a  lower  mean 
annual  temperature  than  the  normal  of  the  latitude  ;  while  on 
the  ocean  the  range  of  annual  oscillation  is  very  small,  the  max- 
ima and  minima  occur  later  in  the  season,  and  the  mean  annual 
temperature  is  higher  than  on  the  continents  on  the  same  lati- 
tudes. Now  it  is  readily  seen  that  the  effect  of  the  general 
circulation  from  west  to  east  around  the  globe  in  the  middle 
and  higher  latitudes  is  not  only  to  throw  the  true  continental 
.and  oceanic  climates  from  the  middle  over  toward  the  eastern 
sides  of  the  continents  and  oceans,  but  also  to  cause  the  west- 
ern sides  of  the  oceans  to  have  a  somewhat  continental  climate 
and  the  western  sides  of  the  continents  to  have  in  some  meas- 
ure an  oceanic  climate,  and  consequently  to  cause  a  great 
contrast  of  climates  between  the  western  and  eastern  sides  of 
the  continents.  Accordingly  Europe,  especially  the  western 
side,  has  a  mean  temperature  a  little  above  the  normal  of  lati- 
tude, small  annual  inequalities  with  the  maxima  and  minima 


1 82  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION 

occurring  later  in  the  season,  and  a  damper  atmosphere  ;  while 
on  the  eastern  side  of  Asia,  on  the  same  latitudes,  the  mean, 
annual  temperature  is  a  little  below  the  normal  of  latitude,  and 
there  are  large  annual  inequalities  of  temperature  with  maxima 
and  minima  occurring  earlier  in  the  season,  and  a  much  drier- 
atmosphere. 

The  mean  annual  temperatures  of  Norway  and  Sweden,  from 
this  cause,  are  about  20°  F.  higher  than  those  of  the  eastern- 
part  of  Siberia,  and  those  of  France  about  15°  higher  than 
those  of  the  Chinese  Empire  on  the  same  latitudes.  Similar 
differences  of  mean  temperature  are  also  found  between  the 
western  and  eastern  sides  of  North  America.  Again,  while  the 
mean  annual  range  of  temperature  in  Norway  and  Sweden  is 
scarcely  as  much  as  35°  F.,  that  of  the  eastern  part  of  Asia  orr 
the  same  latitude  is  more  than  90°.  The  annual  temperature 
ranges,  also,  in  Germany,  are  only  about  half  as  great  as  on  the 
same  parallels  of  latitude  in  the  Chinese  Empire.  Similar  dif- 
ferences are  observed  in  the  annual  inequalities  of  temperature 
between  the  west  and  east  sides  of  North  America,  but  not 
nearly  so  great,  because  the  continent  is  much  narrower.  The 
epochs,  also,  of  midwinter  and  midsummer  occur  about  a  half 
month  later  on  the  west  than  on  the  east  sides  of  the  conti- 
nents, the  former  corresponding  more  nearly  with  those  of 
oceanic,  and  the  latter  with  those  of  continental,  climates. 

In  the  southern  hemisphere  the  continents  do  not  extend  so 
far  into  the  higher  latitudes,  and  the  contrasts  of  climate  be- 
tween the  two  sides  of  the  continents  are  comparatively  small, 
the  tendency  of  the  general  circulation  around  the  globe  being 
to  reduce  the  temperatures  and  all  the  climatic  features  some- 
what to  those  of  the  ocean,  so  that  in  the  southern  parts  of 
South  America  and  of  Africa  there  are  only  small  annual  tem- 
perature ranges. 

In  the  lower  latitudes  of  both  hemispheres  the  annual  tem- 
perature ranges  of  course  are  small,  and  consequently  there  is 
but  little  difference  in  temperature  between  the  two  sides  of 
the  continents,  and  the  principal  differences  here  are  in  the 
mean  annual  temperatures,  those  of  the  ocean  being  consider- 


IN  CONNECTION    WITH  MOUNTAIN  RANGES.  183 

ably  lower,  but  in  consequence  here  of  the  westerly  motion  of 
the  atmosphere  at  the  earth's  surface,  the  eastern  sides  of  the 
oceans  and  the  western  sides  of  the  continents  have  higher 
mean  annual  temperatures  than  the  western  sides  of  the  oceans 
and  the  eastern  sides  of  the  continents.  For  instance,  the 
easterly  winds  of  the  great  Sahara,  and  North  Africa  generally, 
must  tend  to  drive  the  heat  and  the  dryness  westward  toward 
the  Atlantic,  so  that  the  east  side  of  the  Atlantic  here  which 
receives  the  sand  and  dust  from  the  continent,  §  87,  must  have 
a  higher  air  temperature  and  a  drier  air  than  the  west  side. 

IN   CONNECTION  WITH   MOUNTAIN   RANGES. 

123.  If  the  whole  surface  of  the  earth  were  that  of  the 
ocean,  or  any  smooth  homogeneous  surface,  the  calm-belts,  the 
rain-belt,  and  the  dry  zones  would  extend  without  interruption 
entirely  around  the  globe  with  the  same  regularity  which  is 
observed  upon  the  oceans,  and  everywhere  the  same  climatic 
conditions  would  exist  on  the  same  parallels  of  latitude.  But 
on  account  of  the  influence  of  mountain  ranges  in  deflecting 
the  currents  of  the  general  circulation  of  the  atmosphere,  great 
diversities  of  climate  are  found  in  different  places  on  the  same 
parallels  arising  from  this  cause.  The  air  of  the  lower  strata  of 
the  atmosphere  in  the  trade-wind  zone  of  the  North  Atlantic, 
having  a  westerly  motion,  and  impinging  against  the  high  table- 
lands and  mountain  ranges  of  Mexico,  is  deflected  around 
toward  the  north  over  the  southeastern  States  and  up  the 
Mississippi  Valley  into  the  higher  latitudes,  where  it  combines 
with  the  general  easterly  flow  of  these  latitudes,  and  adds  to  its 
strength.  This  completely  breaks  up  the  continuity  of  the 
tropical  calm-belt  and  dry  zone,  so  that  instead  of  a  dry  region 
with  scanty  rainfall,  such  as  is  found  in  North  Africa,  Arabia, 
Persia,  Beloochistan,  and  Cabul,  we  have  on  the  same  parallels 
in  the  southern  and  eastern  United  States  a  region  of  abundant 
rainfall,  and  all  the  way  up  the  Mississippi  Valley  and  in  the 
interior  of  the  continent  there  is  much  more  rain  than  in  the 
interior  of  Asia.  In  consequence  of  this  deflection,  the  trade- 


1 84  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION*. 

winds  of  the  Atlantic  become  nearly  east  winds  in  the  vicinity 
of  the  West  India  Islands,  and  farther  on  in  the  southeastern 
States  and  the  Mississippi  Valley  the  winds  are  southeasterly 
and  then  southerly,  and  the  warm  and  moist  air  of  the  Gulf  of 
Mexico,  being  carried  around  into  higher  and  cooler  latitudes, 
not  only  furnishes  vapor  for  condensation  into  rain,  but  also 
modifies  somewhat  the  temperatures.  There  is,  therefore,  a 
sufficiency  of  rain  here  on  the  parallels  of  the  north  tropical 
dry  zone  for  agricultural  purposes  as  far  as  the  looth  meridian 
west  of  Greenwich. 

The  easterly  current  across  the  Atlantic  Ocean  on  the  mid- 
dle and  higher  parallels,  strengthened  a  little  by  the  deflected 
current  coming  from  the  Gulf  up  the  Mississippi  Valley, 
impinging  against  the  inequalities  of  the  coast  of  Europe,  and 
especially  the  interior  mountain  ranges,  is  partly  deflected  both 
to  the  right  and  to  the  left,  the  one  branch  passing  down 
toward  the  Canaries  and  the  northwest  coast  of  Africa,  joins 
the  general  westerly  flow  in  the  trade-wind  latitudes,  while  the 
other  curves  around  along  the  coast  of  Norway  on  to  Spitz- 
bergen  and  around  to  Greenland. 

In  consequence  of  these  deflections  there  is  a  gyration  of 
air  around  a  central  region  midway  between  America  and  the 
eastern  continent  on  the  parallels  of  the  zone  of  high  pressure, 
and  also  one  around  a  central  area  in  the  vicinity  of  Iceland. 
These  gyrations  are  indicated  by  the  arrows  showing  the  pre- 
vailing directions  of  the  winds  on  Coffin's  charts,19  and  also  by 
the  charts  of  M.  Brault,  based  upon  many  thousands  of  obser- 
vations. From  the  former  of  these  gyrations  it  results  that  the 
northeast  trade-winds  adjacent  to  Africa  seem  to  come  from  a 
more  northerly  direction  and  from  a  higher  latitude  than  they 
do  farther  west,  while  on  the  west  side  of  the  ocean  they 
become  easterly,  and  even  southeasterly,  winds.  The  former 
also  gives  rise  to  the  prevailing  northwest  winds  in  the  part  of 
the  Atlantic  Ocean  adjacent  to  Spain  and  Portugal  and  the 
northwest  coast  of  Africa,  and  the  latter  in  part  to  the  prevail- 
ing southwest  winds  of  the  British  Isles  and  the  coast  of  Nor- 
way, and  the  northeasterly  winds  of  Greenland. 


IN  CONNECTION    WITH  MOUNTAIN  RANGES.  185 

Where  the  general  easterly  current  of  the  middle  latitudes 
impinges  against  the  high  lands  of  the  interior  of  Asia,  com- 
prising the  Kuenlun  and  Himalaya  chains,  the  latter  1300 
miles  in  length,  with  an  average  height  of  18,000  feet,  on  the 
south,  and  the  Great  and  Little  Altai  Mountains  on  the  north, 
with  the  elevated  and  desert  table-lands  containing  the  Desert 
of  Gobi  between  them,  they  are  again  deflected,  not  around 
and  back,  as  on  the  west  coast  of  Europe,  but  to  each  side,  the 
southern  branch  giving  rise  to  prevailing  northwesterly  winds 
over  a  large  region,  including  southeast  Europe  and  southwest 
Russia.  WoeikofT  says:  "  There  is  a  region  comprising  Hun- 
gary, Transylvania,  the  Danubian  Principalities,  and  southwest 
Russia,  in  which  the  prevailing  winds  are  northwest  both  win- 
ter and  summer."  20  These  winds  also  prevail  over  Arabia  and 
Persia,  and  this  deflection  likewise  affects  the  directions  of  the 
regular  monsoons  of  India,  and  its  effect  is  felt  even  at  the 
equator  south  of  Asia,  where  it  gives  rise  to  a  strong  west  wind, 
sometimes  called  the  west  monsoon  of  the  line,  where,  otherwise, 
there  would  be  no  wind  with  an  east  or  west  component  of 
motion. 

124.  In  like  manner,  in  the  lower  latitudes  of  the  South 
Atlantic  Ocean  the  general  westerly  current  of  the  lower  part 
of  the  atmosphere,  on  arriving  at  the  continent  of  South 
America,  and  especially  at  the  high  range  of  the  Andes,  with  a 
mean  elevation  of  nearly  12,000  feet,  is  deflected  around  toward 
the  south  over  Brazil  and  on  southeastward  until  it  enters  and 
combines  with  the  strong  easterly  current  of  the  middle  latitudes 
of  the  South  Atlantic.  Instead,  therefore,  of  the  rainless  zone,  as 
it  exists  on  the  ocean  in  the  trade-wind  and  high-pressure  lati- 
tudes, extending  across  the  continent  of  South  America,  or 
there  being  a  deficiency  of  rain,  as  in  some  other  countries  on 
these  latitudes,  there  is  a  sufficiency  of  rain  over  all  Brazil  and 
the  eastern  side  of  South  America,  up  nearly  to  the  parallel 
of  40°  S. 

The  moisture  for  this  rain  is  furnished  by  the  deflected  cur- 
rents of  warm  and  damp  air  from  the  trade-wind  and  rainy  zone, 
for  the  air  of  the  trade-winds  is  damp,  but  the  zones  of  trade- 


1 86  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION.. 

winds  on  the  oceans  are  rainless,  because  the  conditions,  which 
are  found  on  the  uneven  land  surface,  for  producing  ascending 
currents  and  vapor  condensation  are  wanting  on  the  oceans. 
On  account  of  this  deflection,  instead  of  southeasterly  winds, 
as  in  the  ocean  on  the  same  latitudes,  the  prevailing  winds  are 
northeasterly  and  northerly  over  Brazil,  just  as  in  the  southern 
part  of  the  United  States  and  the  Mississippi  Valley  they  are 
southeasterly  and  southerly,  and  the  continuity  of  the  tropical 
calm-belt  and  rainless  zone  of  this  hemisphere  is  also  interfered 
with. 

A  small  part  also  of  the  strong  easterly  current  of  the  mid- 
dle latitudes  is  deflected  around  toward  the  equator  by  the  west 
coast  and  the  mountain  ranges  of  South  Africa,  so  that  there 
is,  on  the  South  Atlantic,  as  on  the  North  Atlantic,  a  gyration 
of  air  around  a  central  area,  midway  between  South  America 
and  Africa,  and  on  the  parallels  of  the  zone  of  high  pressure. 
This  is  also  plainly  indicated  by  the  charts  of  both  Coffin  and 
M.  Brault.  As  a  result  of  this  gyration  the  southeast  trade- 
winds  come  apparently  from  a  higher  latitude  and  have  a  more- 
southerly  direction  on  the  part  of  the  ocean  adjacent  to  Africa, 
and  gradually  assume  a  direction  more  from  the  east  on  longi- 
tudes farther  west.  The  continent  of  Africa  does  not  extend 
far  enough  toward  the  south  pole  to  cause  a  deflection  the  con- 
trary way  and  a  gyration  of  air  in  the  higher  latitudes  of  the 
South  Atlantic,  as  in  those  of  the  North  Atlantic. 

125.  On  the  east  coasts  of  China  and  of  South  Africa,  and 
in  some  measure  on  those  of  New  Guinea  and  Australia,  there 
are  similar  deflections  of  the  trade-winds  by  the  highlands  and 
mountain  ranges  of  these  countries  around  toward  the  middle 
and  higher  latitudes,  where  the  deflected  currents  become  a 
part  of  the  easterly  currents  of  these  latitudes.  For  this  rea- 
son the  winds  on  the  southeast  of  China  and  the  adjacent  sea, 
comprising  the  Philippine  and  the  Ladrone  Islands,  are  more 
from  easterly  and  southeasterly  directions  and  are  damper  tharv 
they  otherwise  would  be,  and  the  rainfall  is  more  abundant. 
This  effect,  however,  is  much  obscured  here  by  the  great  dis- 
turbing influence  of  the  monsoons,  which  introduces  great 


IN  CONNECTION    WITH  MOUNTAIN  RANGES.  1 87 

annual  changss  and  alterations  in  both  the  directions  of  the 
winds  and  the  amount  of  rainfall.  East  of  New  Guinea  and 
Australia  the  normal  direction  of  the  trade-winds  is  changed  to 
one  more  from  the  east  and  northeast,  and  on  the  east  coast  of 
South  Africa  a  similar  but  still  greater  effect  is  produced  upon 
the  direction  of  the  trade-wind.  Consequently  the  calm-belts 
and  dry  zones  are  very  much  broken  up  on  all  these  eastern 
coasts  in  the  lower  latitudes  of  both  hemispheres,  and  great 
climatic  changes  introduced. 

The  easterly  current  over  the  middle  latitudes  of  the  North- 
Pacific,  strengthened  a  little  by  the  deflected  current  on  the: 
east  coast  of  China,  on  arriving  at  the  west  coast  of  North 
America,  is  likewise  in  part  deflected  by  the  coast  and  the 
mountain  ranges,  a  small  part  around  northward  by  Alaska  on 
to  Behrings  Strait,  but  mostly  around  to  the  right  along  the 
coast  of  California  and  on  to  the  latitudes  of  the  northeast 
trades,  where  it  becomes  a  part  of  the  westerly  current  in  the 
direction  of  China.  This  latter  deflection  gives  rise  to  a  pre- 
dominance of  northwesterly  and  northerly  winds  along  the 
coast  of  California  and  the  adjacent  sea,  and  to  a  more  north- 
erly direction  of  the  trade-winds  west  of  Mexico  for  some  dis- 
tance westward,  and  to  a  breaking  up  of  the  continuity  of  the 
calm-belt  and  the  dry  zone  which  would  otherwise  exist  here 
on  those  latitudes. 

In  the  South  Pacific  Ocean  the  strong  easterly  current  of 
the  middle  latitudes  impinges  against  the  high  mountain  range 
of  the  Andes,  and  a  part  of  it  is  deflected  around  by  the  coasts 
of  Chili  and  Peru  and  over  the  adjacent  ocean  until  it  likewise 
joins  the  general  westerly  current  in  the  latitudes  of  the  south- 
east trade-winds.  On  this  account  these  winds  seem  to  extend 
much  farther  south  here  and  are  more  southerly  than  in  the 
trade-wind  zone  farther  west,  where  the  direction  becomes 
more  from  the  east.  Here,  consequently,  the  deflected  current 
breaks  through  the  belt  of  high  pressure  of  these  latitudes  and 
interferes  with  the  continuity  of  the  rainless  zone  of  the  tropi- 
cal calm-belt  and  southeast  trade-winds. 

126.  In  consequence  of  the  general  circulation  of  the  at- 


1 88  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION. 

mosphere,  both  the  temperature  and  the  amount  of  rainfall  are 
often  different  on  the  two  sides  of  a  mountain  range,  especially 
where  the  direction  of  this  range  is  normal  to  the  prevailing 
direction  of  the  wind.  The  current,  in  passing  over  the  moun- 
tain, carries  the  aqueous  vapor  up  to  a  higher  altitude  where  it 
is  cooled  by  the  expansion  of  the  ascending  air  and  condensed, 
just  as  in  the  case  of  a  vertically  ascending  current  in  the  equa- 
torial rain-belt ;  so  that  on  the  windward  side  of  the  mountain 
there  is  an  unusual  amount  of  rainfall.  This  is  especially  the 
case  if  the  rain-producing  currents  pass  to  the  mountain  side 
from  the  ocean,  where  the  air  is  generally  more  nearly  satu- 
rated, and  more  especially  if  it  passes  from  a  warmer  ocean 
to  a  colder  district,  for  then  the  air  has  greater  capacity  for 
moisture,  and  is  liable  to  be  very  nearly  saturated  before  it 
reaches  the  mountain  side  and  begins  to  ascend.  On  the  lee- 
ward side  the  air  descends  to  a  lower  level,  and  if  it  were  even 
.saturated  with  aqueous  vapor  in  crossing  the  top  of  the  range, 
it  soon  becomes  unsaturated,  and  consequently  there  is  no 
longer  any  condensation  or  rainfall,  so  far  as  it  depends  upon 
the  general  current  passing  over  the  mountain,  and  there  can 
therefore  be  no  rainfall  on  this  side,  unless  it  arises  from  other 
local  and  temporary  causes. 

In  the  general  circulation  of  the  atmosphere,  we  have  seen 
that  the  average  or  resultant  direction  of  the  winds  in  the  mid- 
<dle  and  higher  latitudes,  at  the  earth's  surface  and  in  the  lower 
strata  of  the  air,  is  nearly  from  west  to  east,  and  in  the  zones 
of  the  trade-winds  there  is  a  large  west  component  of  motion. 
Hence  in  the  case  of  all  high  mountain  ranges  extending  north 
and  south,  or  approximately  so,  especially  in  the  case  of  coast 
ranges,  the  west  sides  of  these  ranges,  in  the  middle  and  higher 
latitudes,  should  be  the  rainy  sides,  and  the  east  sides  the  dry 
sides,  and  the  reverse  in  equatorial  and  tropical  latitudes. 
Hence  in  the  northern  part  of  California,  in  Oregon,  Washing- 
ton Territory,  and  Alaska,  along  the  Pacific  coast,  there  is  an 
abundant  annual  rainfall,  of  from  50  to  75  inches  and  more,  as 
may  be  seen  from  Loomis's  rain  chart,22  caused  by  the  coast 
:ranges  of  mountains,  the  winds  in  this  case  coming  directly 


IN  CONNECTION    WITH  MOUNTAIN  RANGES.  1 89* 

from  the  ocean.  After  passing  the  coast  ranges  in  these  high 
and  cool  latitudes  the  amount  of  aqueous  vapor  left  in  the  air 
is  very  much  diminished,  so  that  farther  on  there  is  but  little 
rainfall,  and  especially  east  of  the  main  Rocky  Mountain 
range.  There  is,  consequently,  a  large  area  east  of  this  range, 
extending  to  about  the  looth  meridian  west  from  Greenwich, 
over  which  the  amount  of  annual  rainfall  is  small.  Farther 
east,  over  the  United  States  and  Canada,  the  vapor  for  pro- 
ducing rain,  as  has  been  explained,  comes  mostly  from  the  Gulf 
of  Mexico,  and  the  causes  of  the  ascending  currents  necessary 
to  give  rise  to  condensation  and  rainfall  depend  mostly  upon 
the  local  and  temporary  disturbances  of  ordinary  rain-storms, 
and  but  little  upon  mountain  ranges. 

In  western  Europe,  where  the  westerly  winds  from  the 
Atlantic  Ocean  first  strike  the  continent,  especially  on  the  west 
sides  of  the  mountain  ranges,  even  those  near  the  ocean  of 
only  moderate  height,  and  on  the  west  side  of  the  Caucasus 
Mountains  on  the  east  side  of  the  Black  Sea,  over  which  the 
winds  pass  before  reaching  them,  there  is  mostly  an  abundant 
annual  rainfall ;  while  in  the  interior  parts  of  Asia,  especially  in 
Tartary  and  Mongolia,  the  amount  of  annual  rainfall  is  scant, 
the  aqueous  vapor  having  been  mostly  condensed  and  having 
fallen  in  rain,  in  passing  over  the  mountain  ranges  of  Europe,, 
and  in  ascending  currents  in  ordinary  rain-storms,  before  reach- 
ing them. 

On  the  west  side  of  the  Andes,  south  of  the  parallel  of  about 
35°,  in  Chili  and  Patagonia,  the  amount  of  rainfall  is  very  great, 
arising  from  the  upward  deflection  of  the  moist  and  strong  air 
currents  of  these  latitudes,  coming  directly  from  the  ocean; 
while  on  the  east  side  of  the  range  of  the  Andes  here,  there 
is  scarcely  any  rain. 

27.  In  the  trade-wind  latitudes  of  both  hemispheres, 
where  the  air,  on  account  of  its  west  component  of  motion,  is 
deflected  upward  by  the  mountain  ranges  of  Central  America,, 
and  the  Andes  in  South  America,  the  rainfall  is  very  greatr 
while  on  the  opposite  sides,  especially  in  Peru,  and  on  the 
ocean  adjacent,  there  is  scarcely  any  rain,  although  it  is  said 


19°  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION'. 

that  the  air  here  is  often  nearly  or  quite  saturated  with  aqueous 
vapor,  and  that  fogs  and  mists  frequently  occur.  At  the  head- 
waters of  the  Amazon  on  the  east  side  of  the  very  high  range 
of  the  Andes,  and  where  the  warm  and  very  moist  air  currents 
of  the  zone  of  the  southern  trade-winds  strike,  the  amount  of 
annual  rainfall  is  especially  great,  but  this  is  increased  by  the 
rainfall  of  the  equatorial  calm-belt,  which  oscillates  here  through 
a  considerable  range  of  latitude,  and  so  increases  the  annual 
rainfall  over  the  whole  of  this  range.  On  the  east  coasts  also 
of  South  Africa,  of  Madagascar,  and  of  Australia,  within  the 
.zone  of  the  southeast  trade-winds,  and  which  on  the  oceans  is 
a  rainless  zone,  there  are  considerable  rainfalls,  while  on  the 
west  sides  there  are  scant  rainfalls,  if  not  an  almost  entire 
•deficiency,  and  the  latter  is  the  case  all  the  way  through  the 
interior  of  Australia  to  the  western  coast. 

The  large  annual  rainfall  on  the  eastern  coast  of  China  is 
'due  in  part  to  the  same  cause,  but  mostly  perhaps  to  the  sum- 
mer monsoon  which  draws  the  warm  and  moist  air  from  the 
adjacent  ocean  over  the  mountain  ranges  in  toward  the  interior 
of  the  continent. 

On  both  sides  of  the  Rocky  Mountains  and  the  Andes  on 
the  parallels  from  30°  to  40°,  there  is  scarcely  any  rainfall,  for 
these  being  the  parallels  of  little  or  no  easterly  or  westerly  mo- 
tion of  the  atmosphere,  there  is  no  upward  deflection  of  the 
air  on  either  side,  and  besides,  being  in  the  belt  of  high  pres- 
.-sure,  there  is  a  tendency  in  the  air  to  settle  down  toward  the 
surface,  and  hence  there  is  little  rainfall. 

28.  Wherever,  on  account  of  the  prevailing  currents,  there 
is  a  wet  and  a  dry  side  to  the  mountains,  the  dry  side  is  the 
warmer.  The  air  in  ascending  on  the  wet  side,  until  condensa- 
tion takes  place,  cools  at  the  same  rate  with  increase  of  altitude, 
as  it  is  warmed  on  the  other  side  in  falling  through  the  same 
distance.  But  pfter  condensation  commences,  as  may  be  seen 
from  Table  III,  the  rate  of  cooling  of  ascending  air  is  much  less, 
especially  where  the  temperature  is  high,  as  in  the  lower  lati- 
tudes; while  on  the  other  side,  where  the  air  descends  from  its 
highest  level  to  that  where  condensation  commences,  the  rate 


IN  CONNECTION    WITH  MOUNTAIN  RANGES.  IQI 

is  the  same  as  that  of  dry  air,  except  that  it  is  diminished  a 
little  by  the  evaporation  of  the  cloud-particles  immediately 
after  it  first  begins  to  descend.  Suppose  the  height  of  the 
range  is  3000  meters,  but  that  the  condensation  begins  at  the 
altitude  of  1000  meters.  Then  if  the  rate  of  cooling  on  the 
average,  while  the  air  is  ascending  and  condensation  is  taking 
place,  is  o°.5  C.  for  each  100  meters  of  ascent,  the  air  is  cooled 
in  this  ascent  10°,  while  in  descending  on  the  other  side  to  the 
same  level  of  incipient  condensation  in  ascending,  the  increase 
of  temperature  is  20°,  or  nearly,  and  so  there  is  a  gain  of  nearly 
10°  C.  of  temperature  from  the  time  the  air  left  the  level  of  in- 
cipient condensation  on  the  one  side  until  it  descended  to  the 
same  level  on  the  other  side.  Since  the  rate  of  cooling  below 
this  level  as  the  air  ascends,  is  exactly  the  same  as  that  of 
increase  of  temperature  in  descending  on  the  other  side  through 
the  same  distance,  of  course  there  is  the  same  difference  of 
temperature  at  the  earth's  surface  between  the  two  sides,  if  the 
surface  on  each  side  has  the  same  level,  as  there  is  at  the  level 
ot  incipient  condensation  as  the  air  ascends.  The  effect  is  that 
of  a  temporary  foe/in  to  be  considered  farther  on,  and  is  here 
a  permanent  effect  continuing  through  the  year,  with  most 
probably  a  considerable  annual  inequality,  since  the  strength 
of  the  general  air  currents  upon  which  it  depends  is  greater  in 
winter  than  in  summer.  Of  course  the  full  effect,  as  computed 
above,  is  never  reached,  since  the  computation  assumes  that 
the  air  is  cooled  and  heated  simply  by  expansion  and  compres- 
sion ;  but  the  temperature  depends  upon  a  balancing  of  the 
rates  of  absorption  and  radiation,  and  the  radiation  of  the 
warm  air  on  the  one  side  is  greater  than  that  of  the  cold  air  on 
the  other  side,  and  consequently  the  difference  is  a  little  less 
than  that  of  the  computation.  As  the  air  flows  away  from  the 
base  of  the  mountain  range  eastward,  of  course  the  tempera- 
ture becomes  less  until  it  is  reduced  to  that  depending  upon 
the  local  conditions  and  independent  of  the  foehn  effect  of  the 
^distant  mountain. 

In  accordance  with  what  precedes,  there  is  a  belt  close  along 
the  eastern  side  of  the  Rocky  Mountain  range,  with  a  mean 


IQ2  CLIMATIC  INFLUENCES  OF  THE  GENERAL  CIRCULATION.. 

temperature  above  that  of  the  same  latitude  farther  east,  and 
which  is  sensibly  felt  to  a  considerable  distance  over  the  plain, 
and  this  is  especially  the  case  in  the  winter  season.  Accord- 
ingly the  coldest  winds  in  winter  at  Denver  and  Cheyenne,  and 
other  places  similarly  situated  on  the  east  side  of  the  Rocky 
Mountain  range,  are  not  the  northerly  or  northwesterly  winds, 
but  those  from  a  northeasterly  direction.  It  is  also  said  that 
the  mean  winter  temperature  at  Georgetown,  Colorado,  close 
to  the  base  of  the  mountain,  is  milder  than  that  of  Denver, 
some  forty  miles  farther  east,  although  the  elevation  of  the 
former  is  nearly  4000  feet  greater. 

A  similar  effect  seems  to  be  produced  by  the  range  of  the 
Andes  in  South  America.  According  to  Dr.  Gould's  isother 
mal  chart  of  the  mean  annual  temperature  of  the  southern  part 
of  South  America,31  the  temperature  immediately  east  of  the 
range  is  several  degrees  of  the  Centigrade  scale  higher  than 
on  the  west  side,  and  also  considerably  higher  than  that  farther 
east  on  the  same  parallels,  at  least  north  of  the  parallel  of  40°, 
where  the  continent  is  wide,  and  the  isotherms  are  well  deter- 
mined on  the  eastern  side  of  the  continent. 


CHAPTER  V. 
MONSOONS,   AND   LAND-  AND  SEA-BREEZES. 

INTRODUCTION. 

129.  HAVING  treated  the  general  circulation  of  the  atmos- 
phere with  its  annual  inequalities  or  changes  with  the  seasons, 
arising  from  the  difference  of  temperature  between  the  equa- 
torial and  polar  regions  and  its  annual  variations,  we  come  now 
to  consider  the  less  general,  but  still  often  powerful,  atmos- 
pheric disturbances  arising  from  differences  of  atmospheric  tem- 
perature between  continents  or  islands  and  the  surrounding 
oceans,  or  between  any  region  of  the  earth's  surface,  abnor- 
mally heated  or  cooled,  and  the  surrounding  parts  of  that  sur- 
face. In  the  general  circulation  of  the  atmosphere  the  tem- 
perature difference  upon  which  it  depends  is  permanent,  though 
subject  to  large  annual  inequalities  ;  but  in  these  secondary  and 
less  general  disturbances  there  is  little  or  no  permanent  tern 
perature  disturbance,  independent  of  the  annual  and  diurnal 
changes  and  reverses,  and  so  they  are  mostly  of  the  latter  charac- 
ter, and  these  give  rise  to  annual  and  diurnal  alternations  of 
direction  and  velocity  of  motion.  The  former  of  these  alter- 
nations are  called  monsoons,  and  the  latter  land-  and  sea-breezes^ 

It  has  been  shown,  §  68,  that  in  the  lower  latitudes  the  mean 
annual  temperature  of  the  continents  is  greater  than  that  of 
the  oceans  on  the  same  latitudes,  and  the  reverse  in  the  higher 
latitudes.  There  is,  consequently,  a  permanent  difference  of 
temperature  between  the  continents  and  the  oceans  in  the  equa- 
torial regions,  the  mean  temperatures  of  the  former  being  the 
greater,  but  this  vanishes  in  the  middle  latitudes,  and  becomes, 
reversed  in  the  polar  latitudes.  This  difference,  however,  at 
most,  is  small  in  comparison  with  the  great  annual  changes  and 

i93 


194  MONSOONS,  AND  LAND-  AND   SEA-BREEZES. 

reversals  of  differences,  except  near  the  equator,  where  these 
annual  changes  are  small.  These  permanent  differences  of  tem- 
perature must  give  rise  to  corresponding  permanent  atmos- 
pheric circulations,  with  motions  of  the  lower  part  of  the  atmos- 
phere from  the  colder  to  the  warmer  region,  and  the  reverse 
above,  to  which  are  superadded  the  usually  greater  disturbances 
depending  upon  the  annual  variations  of  temperature.  Mon- 
soons are  usually  defined  to  be  winds  which  blow  six  months 
in  one  direction  and  the  other  six  months  in  the  contrary  direc- 
tion ;  but  this  complete  reversal  takes  place  only  where  there  is 
no  permanent  atmospheric  disturbance  of  any  kind,  such  as  that 
of  the  general  circulation  with  its  various  deflections  by  conti- 
nents and  mountain  ranges,  or  from  the  permanent  part  of  the 
monsoon  influence  just  referred  to.  The  monsoons,  therefore, 
are  generally  not  complete  reversals  of  direction  with  interven- 
ing intervals  of  little  or  no  velocity,  but  the  directions  at  the 
different  seasons  may  change  less  than  a  quadrant,  and  the 
strength  of  the  winds  may  vary  considerably  at  different  sea- 
sons, but  not  entirely  vanish.  In  fact,  where  there  are  strong 
perennial  winds,  the  monsoon  influence  may  be  such  as  to 
merely  change  a  little  the  strength  and  direction  of  these  winds, 
one  way  at  one  season  of  the  year  and  the  contrary  way  at  the 
opposite  season. 

130.  The  temperature  differences  or  gradients  upon  which 
the  monsoons  depend  are  not  those  of  the  absolute  tempera- 
tures, but  the  gradients  of  the  differences  between  these  and 
the  normal  temperatures  of  latitude  of  summer  and  of  winter. 
From  the  temperature  gradients  of  the  latter  or  normal  tem- 
peratures of  latitude  arise  the  general  atmospheric  circulations 
of  the  two  hemispheres,  so  that  these  must  not  be  again  taken 
in  as  a  part  of  the  monsoon  influences ;  but  these  latter  must 
depend  upon  differences  or  temperature  gradients  in  the  ab- 
normals  of  temperature,  that  is,  departures  of  temperature  from 
the  normals  of  latitude,  for  without  such  departures  we  should 
have  no  monsoon  influences,  but  simply  the  undisturbed  gen- 
eral atmospheric  circulation,  with  velocities  a  little  greater  in 
winter  than  in  summer,  but  no  monsoon.  For  instance,  the 


INTRODUCTION.  IQ5 

interior  of  a  large  continent  may  be  much  warmer  than  the 
polar  and  much  colder  than  the  equatorial  side,  but  still  the 
temperature  gradients  arising  from  such  differences  may  not 
form  any  part  of  the  monsoon  influence.  But  if  there  is  an 
increase  or  decrease  from  the  interior  outward  of  the  departures 
of  actually  existing  temperatures  from  the  normals  of  latitude, 
then  we  have  a  temperature  disturbance  which  gives  rise  to  a 
monsoon,  or  at  least  to  a  monsoon  influence. 

131.  Land-  and  sea-breezes,  at  least  of  small  islands,  are  sim- 
ilar to  monsoons,  the  latter  being  a  regular  alternation,  more 
•or  less  complete,  of  the  direction  of  the  wind  between  summer 
and  winter,  and  the  former  between  day  and  night ;  but  the 
lengths  of  the  periods  of  the  alternations  are  very  different. 
Jn  the  case  of  continents  the  land-  and  sea-breezes  are  sensible 
along  the   coasts   only,  where  the  temperature  gradients  are 
•greatest ;  for  the  periods  of  alternation  are  so  short  that  a  com- 
plete system  of  interchanging  motions  between  the  ocean  and 
the  land,  extending  into  the  interior  of  the  continent,  cannot 
be  formed  and  reversed  every  day,  and  so  the  winds  in  this 
•case  generally  extend  only  a  short  distance  either  inland  or  out 
on  the  ocean.     In  the  case  of  a  small  island,  however,  where  a 
•complete  interchanging  circulation  can  be  inaugurated   in   a 
short  time,  there  is  little  difference  between  the  land-  and  sea- 
breezes  and  the  monsoons  of  continents,  except  in  their  extent 
.and  in  the  periods  of  alternation. 

132.  The  strength  of  the  monsoon,  or  of  the  land-  and  sea- 
breeze,  depends  very  much  upon  the  nature  of  the  surface  of 
the  continent.     In  the  case  of  a  perfectly  flat  continent  with 
no  highlands  or  mountain  ranges,  there  would,  of  course,  be  an 
interchange  of  air  between  it  and  the  ocean  in  case  of  differ- 
ence of  temperature,  that  of  the  lower  part  moving  toward  the 
^warmer  region,  and  that  of  the  upper  part  away  from  it ;  but 
the  monsoon  effects  would  be  comparatively  small,  and  would 
not  at  all  have  the  great  strength  of  surface  winds  which  is 
usually  observed.     The  interchange  would  be  mostly  in  the 
;great  mass  of  air  above,  and  no  strong  motion  would  take  place 
.at   the   earth's  surface.     In  this  case,  also,  the  land-  and  sea- 


196  MONSOONS,  AND  LAND-  AND   SEA-BREEZES. 

breezes  have  but  little  strength,  and  are  felt  near  the  coasts 
only,  but  they  are  very  much  increased  in  strength,  and  are  felt 
at  a  much  greater  distance,  where  there  are  hillsides  and  moun- 
tain slopes  near  the  coast. 

In  the  annual  and  diurnal  oscillations  of  temperature  the 
amplitudes  are  small  on  the  ocean  surface,  and  in  the  air  at  all 
altitudes  above  it,  and  also  in  the  great  mass  of  air  over  the 
continent  except  in  a  stratum  next  the  earth's  surface,  of  small 
depth  in  comparison  with  that  of  the  whole.  The  monsoon 
effects,  therefore,  depend  mostly  upon  the  temperature  differ- 
ences between  the  continent  and  the  ocean  of  only  a  compara- 
tively thin  stratum  of  the  atmosphere  next  the  earth's  surface,, 
of  which  the  part  over  the  continent  is  very  much  heated  above, 
or  cooled  below,  that  of  the  ocean.  The  temperature  differ- 
ences of  such  a  stratum,  over  a  perfectly  level  continent,  even 
if  they  were  very  great,  would  give  rise  to  very  little  horizontal 
disturbance  of  the  atmosphere.  If  this  stratum  over  the  con- 
tinent were  greatly  heated,  it  might  give  rise  to  the  unstable 
state,  from  which  would  result  numerous,  but  very  small,  local 
eruptions  through  the  strata  above,  but  no  sensible  monsoon-; 
effects.  On  the  other  hand,  if  it  were  cooled  down  to  a  very- 
low  temperature,  the  increased  density  would  tend  mostly  to^ 
keep  it  next  the  earth's  surface,  and  there  would  be  scarcely 
any  tendency  to  flow  away  laterally  toward  the  warmer  ocean. 
But  if  the  surface  of  the  continent  is  convex,  or  if  it  has  high- 
lands with  long  slopes,  or  the  interior  is  in  almost  any  way 
considerably  elevated  above  sea-level,  the  tendency  in  the  case 
of  the  summer  monsoon  to  flow  in  from  the  ocean  toward  the 
interior  of  the  continent,  or  the  reverse  in  that  of  the  winter 
monsoon,  is  very  much  increased.  The  same  is  true  with  re- 
gard to  land-  and  sea-breezes  where  there  are  mountain  eleva- 
tions near  the  coast. 

133.  The  reason  of  this  can,  perhaps,  be  made  clearer  by 
assuming  an  analogous  case,  but  one  which  will  be  more  easily 
understood.  If  a  perfectly  level  plain  were  covered  with  a 
stratum  of  water,  there  would,  of  course,  be  some  flow  of  water 
in  all  directions  from  the  interior  outward  ;  but  unless  the  depth. 


INTRODUCTION. 

were  considerable  in  comparison  with  the  extent  of  the  plain, 
the  current  might  not  be  perceptible  except  near  the  outer 
part.  But  if  the  same  depth  of  water  were  placed  upon  the 
surface  of  a  continent  with  an  elevated  interior  having  long 
declining  slopes  from  the  interior  outward,  the  rapidity  of  the 
rush  of  water  would  be  very  great,  and  somewhat  in  propor- 
tion to  the  steepness  of  these  slopes.  The  case  is  somewhat 
similar  where  there  is  a  stratum  of  air  next  the  earth's  surface 
abnormally  cold  and  dense  in  comparison  with  the  air  above  it 
and  over  the  ocean.  If  the  earth's  surface  is  flat  there  is  little 
tendency  in  this  air  to  move  in  any  direction,  but  if  it  rests 
upon  declining  slopes,  this  tendency,  as  in  the  case  of  water,  is 
very  much  increased.  Of  course  the  absolute  tendencies  in 
the  case  of  water  and  the  abnormally  dense  stratum  of  air  are 
very  different,  the  former  being  due  to  the  force  of  the  whole 
pressure  of  the  fluid  down  an  inclined  plane,  but  the  other 
merely  to  the  increased  pressure  arising  from  the  diminished 
temperature  and  increase  of  density.  The  relative  tendencies, 
however,  for  different  surfaces  are  the  same  in  both  cases,  and 
.somewhat  in  proportion  to  the  steepness  of  the  declining  sur- 
face. 

The  very  reverse  of  this  is  the  case  where  the  stratum  of  air 
next  the  earth's  surface  is  abnormally  heated  in  comparison 
with  the  temperature  of  the  air  above  and  around  about.  If 
the  excess  of  temperature  in  this  case  is  the  same  as  the  defi- 
ciency in  the  other,  the  tendency  now  to  flow  from  all  sides  to- 
ward the  interior  up  the  slopes  is  exactly  equal  to  the  tendency 
to  flow  outward  and  down  these  slopes  in  the  other  case.  There 
being  now  a  deficiency  of  pressure  in  the  warm  rarefied  stratum, 
where  this  rests  upon  an  inclined  surface,  the  greater  pressure 
of  the  heavier  air  everywhere  else  at  the  same  level  tends  to 
drive  the  lighter  surface  air  up  the  slopes  with  the  same 
force  with  which  it  descends  in  the  other  case,  both  depending 
upon  the  same  difference  of  density  between  the  stratum  and 
the  air  generally  at  the  same  levels. 

The  case  of  the  warm  and  rarefied  air  ascending  on  the  slopes 
is  somewhat  similar  to  that  of  warm  air  ascending  in  a  flue.  If 


MONSOONS,  AND   LAND-   AND    SEA-BREEZES. 

the  flue  is  horizontal,  although  the  air  within  is  kept  much 
warmer  than  that  of  the  flue,  and  the  outside  air  generally,  the 
warmer  air  gradually,  but  very  slowly,  passes  out  of  the  flue 
and  allows  other  air  to  take  its  place  ;  but  if  it  is  only  a  little  in- 
clined, the  air  ascends  the  incline  and  escapes  rapidly  from  the 
higher  end,  and  the  more  so  the  greater  the  differences  of 
temperature,  the  length  of  the  tube,  and  the  steepness  of  the 
inclination.  So  the  tendency  of  the  warmer  stratum  of  air  to< 
flow  up  an  inclined  surface  increases  with  increasing  differences. 
of  temperature,  and  increasing  length  and  steepness  of  slope. 

134.  There  is  also  another  consideration  in  connection  with 
the  subject  of  the  monsoon  influence  of  highlands.  The  ten- 
dency of  air  to  ascend  or  descend  and  to  give  rise  to  ascending 
or  descending  currents  depends  upon  differences  of  temperature 
between  the  air  and  that  of  the  surrounding  regions  at  the  same- 
level.  But  it  is  a  matter  of  observation  that  the  temperature 
of  highlands,  and  especially  of  high  plateaus,  in  summer,  is. 
nearly  as  great  as  that  on  plains  near  sea-level.  The  tempera- 
ture, also,  for  the  altitudes  above  the  surface,  at  least  to  a  con- 
siderable height,  must  be  much  greater  than  that  of  the  sur- 
rounding air  at  the  same  levels,  since  the  rate  of  decrease  of 
temperature  with  increase  of  altitude  above  the  surface  of  the 
plateau  is  somewhat  the  same  as  above  any  plain  near  sea-leveL 
If  a  portion  of  air,  therefore,  either  on  a  horizontal  plane  or  a 
slope  near  sea-level  is  only  a  little  warmer  than  the  surrounding 
air  on  the  same  level,  it  tends  to  ascend  and  to  give  rise  to  an 
ascending  current ;  but  if  air  at  the  same  temperature  is  high 
up  on  some  mountain  side  or  plateau,  this  tendency  is  much 
increased,  because  now  the  difference  of  temperature  between 
this  air  and  the  surrounding  air  at  a  distance  on  the  same  level 
is  much  greater. 

If  a  tall  flue  with  a  temperature  only  a  little  raised  above  the 
surrounding  temperatures  at  sea-level  were  elevated  to  the  top 
of  a  high  mountain,  where  the  surrounding  air  is  much  colder 
and  more  dense,  the  draught  of  the  flue  would  be  very  much  in- 
creased. So  the  wide  column  of  air  of  higher  temperature  over 
a  high  plateau  and  extending  up  to  a  considerable  height  above 


IN  TROD  UCTIOtV.  1 99 

the  surface  has  a  much  greater  tendency  to  ascend  than  a  simi- 
lar one  of  the  same  temperature  on  a  low  plane  near  sea-level. 

This  effect,  however,  is  felt  mostly  in  the  summer  monsoon 
influence,  for  in  winter  the  temperature  of  the  plateau  is  not  so 
much  below  surrounding  temperatures  as  it  is  above  them  in 
the  summer. 

135.  In  accordance  with  the  preceding  vie-w  of  the  principal 
cause  of  monsoons  and  land-  and  sea-breezes,  it  is  seen  from  ob- 
servation that  all  the  great  monsoons  and  the  strongest  land- 
and  sea-breezes  are  found — the  former  in  countries  and  on  oceans 
adjacent  to  high  mountain  ranges,  and  the  latter  along  coasts 
with  high  mountains  in  the  background.  Neither  the  heated 
interior  in  summer  of  the  Great  Sahara  of  northern  Africa  nor 
of  Arabia  and  Persia,  which  is  considered  the  warmest  region 
on  the  globe,  causes,  during  this  season  of  the  year,  any  con- 
siderable indraught  of  air.  It  is  true  that  at  this  season  the  north- 
westerly winds  prevail  a  little  more  on  the  northwest  coast  of 
Africa  and  the  ocean  adjacent,  due,  no  doubt,  to  the  influence 
of  the  highly  heated  desert  of  the  Sahara ;  but  over  Arabia  and 
Persia  the  northwest  winds  continue  to  blow  almost  incessantly 
during  June  and  July,  away  from  the  heated  interior  toward 
the  Arabian  Sea,  though  at  times  they  are  quite  light.  Even 
at  this  season  the  tendency  to  flow  in  towards  this  heated  dis- 
trict is  not  sufficient  to  overcome  the  northwest  wind  of  this 
region  arising  from  the  deflection  around  the  elevated  regions 
of  Asia  (§  123).  The  monsoon  influence,  therefore,  of  countries 
mostly  level  without  an  elevated  interior,  however  highly  they 
may  become  heated  in  summer  or  cooled  in  winter,  is  not  very 
great. 

With  regard  to  land-  and  sea-breezes  Mr.  Laughton  says : 3a 

"  This  seems  to  be  sufficiently  established  by  facts,  that  the  sea-breeze 
nowhere  blows  with  any  great  strength,  except  where  there  are  mountains  in 
the  background  ;  and  that  these  mountains  are,  during  the  afternoon,  when 
the  sea-breeze  has  gotten  well  home  to  them,  constantly  enveloped  in 
mist  or  storm.  The  Blue  Mountains  of  Jamaica  afford  the  best  illustra- 
tion of  this ;  and  it  is  on  the  coast  of  Jamaica,  more  especially  of  Port 
Royal,  that  the  sea-breeze  has  a  force  unknown  anywhere  else." 


20O  MONSOONS,  AND  LAND-  AND   SEA-BREEZES. 

In  the  same  connection  it  is  said  : 

'  "  As  a  matter  of  geographical  fact,  the  land-breeze  has  nowhere  any- 
noticeable  strength  unless  there  are  mountains  in  the  immediate  neigh- 
borhood." 

136.  In  the  case  of  the  summer  monsoon,  where  the  interior 
of  the  country  is  so  elevated  that  the  current  ascends  the  slopes 
to  an   altitude  where  condensation  of  the  vapor  takes  place, 
the  latent  heat  of  condensation  adds  much  strength  to  the  cur- 
rent, just  as  in  the  case    of  the  trade- winds,  in  which  their 
strength  is  increased  by  the  latent  heat  of  condensation  in  the 
equatorial  rain-belt.     On  this  account  the  summer  monsoon  of 
the  North  Indian  Ocean  is  much  stronger  than  the  winter  mon- 
soon :  so  much  so,  that  the  southwest  monsoon  is  often  spoken 
of  as  The  Monsoon,  the  northeast  monsoon  being  insignificant 
in  comparison  with  it.     Notwithstanding  the  trade-wind  is  com- 
bined with  the  monsoon  effect,  the  resultant  of  both  produces 
in  the  Arabian  Sea  only  a  gentle  and  steady  breeze  during  the 
winter  season  ;  whereas  the  southwest  monsoon  of  the  summer 
is  a  steady  gale   of  so   great  strength   that  it  is  impossible  for 
even  steamers  to  force  a  passage  from  Bombay  to  the  Gulf  of 
Aden  in  June  and  July. 

In  all  cases,  also,  of  extraordinarily  strong  sea-breezes,  there 
are  high  mountain  elevations  near  the  coast  on  which  there  is  a 
vast  amount  of  condensation  and  precipitation  of  rain  at  the 
time. 

THE   MONSOONS   OF  ASIA   AND  THE  INDIAN   OCEAN. 

137.  In  no  other  part  of  the  world  are  the  conditions  for  a 
powerful  monsoon   influence  so  favorable,  and  the  strength  of 
the  monsoons  produced   so  great,  as  in  India  and  the  North 
Indian  Ocean.     The  Himalayas  on  the  north  with  an  east  and 
west  extent  of  1300  miles  and  an  average  height  of  18,000  feet, 
the  parallel  Kuenlun  range  still  farther  north,  much  greater  in 
extent  but  of  less  height,  with  the  high  plateaus  of  Thibet  and 
Cashmere  between,  and  beyond  these  yet  the  vast  and  elevated 
deserts  of  the  interior  of  Asia  between  the  Kuenlun  and  Altai 


THE  MONSOONS  OF  ASIA    AND    THE  INDIAN  OCEAN.  2OI 

;ranges,  together  with  the  warmth  and  great  capacity  of  the  air 
for  moisture  over  India  and  the  North  Indian  Ocean,  for  reasons 
just  given  in  the  preceding  pages,  all  combine  to  add  strength 
to  the  monsoons,  especially  those  of  the  summer  season.  As 
the  sun  in  early  summer  approaches  the  northern  tropic,  the 
air  of  the  Himalayan  southern  slopes  and  the  desert  of  Gobi 
and  the  sunburned  plains  of  Central  Asia  becomes  warmed 
up  to  a  temperature  much  above  that  of  the  adjacent  and  sur- 
rounding air  at  a  distance  on  the  same  level,  and  so  a  powerful 
centripetal  and  ascending  tendency  is  induced,  by  which  the  air 
is  drawn  in  toward  the  centre  of  warmth  and  rarefaction  from 
all  sides,  but  especially  from  the  equatorial  side,  where  the  in- 
fluence is  felt  even  beyond  the  equator.  For  there  is  not  only 
the  tendency  of  the  heated  stratum  of  air  in  contact  with  the 
southern  slopes  to  ascend,  but  the  air  over  the  whole  of  the 
•elevated  part  of  Central  Asia,  not  only  near  the  surface,  but  up 
to  a  considerable  altitude,  being  warmer  than  that  of  the  sur- 
rounding regions  on  the  same  level,  it  has  a  strong  tendency  to 
rise  up  and  leave  a  partial  vacuum  into  which  air  from  all  sides 
flows  to  take  the  place  of  that  which  is  continually  ascending. 

The  warmth  of  the  air,  and  consequently  the  monsoon 
influence,  is  much  increased  in  summer  by  the  latent  heat  given 
out  in  the  condensation  of  the  aqueous  vapor  in  the  almost 
or  quite  saturated  air  at  the  beginning  of  its  ascent,  for,  being 
of  high  temperature  over  India  and  the  adjacent  ocean,  its 
capacity  for  moisture  is  very  great,  and  this  is  condensed,  not 
only  as  it  ascends  the  southern  slopes  to  the  general  height 
of  the  Himalayas,  but  still  beyond  in  its  further  ascent  over 
the  plateaus  of  Thibet  and  Cashmere,  where  the  amount  of 
rain  during  the  summer  monsoon  is  often  enormous.  Although 
there  would,  no  doubt,  be  a  considerable  monsoon  influence  in 
the  case  of  perfectly  dry  air,  yet  the  principal  part  of  the 
energy  in  the  summer  monsoons  of  India  is  probably  in  the 
aqueous  vapor  of  the  air.  Some  idea  of  the  difference  of 
temperature  between  the  ascending  air  up  the  slopes  of  the 
Himalayas  and  that  over  Thibet  beyond,  and  the  air  of  the 
adjacent  and  surrounding  regions  at  the  same  level,  may  be 


202  MONSOONS,  AND  LAND-   AND    SEA-BREEZES. 

formed  from  an  examination  of  Table  III.  From  this  it  is  seen- 
that  the  average  rate  of  decrease  of  temperature  with  increase 
of  elevation  in  ascending  air,  even  up  to  great  altitudes,  would 
be  only  about  o°.4  C.  in  each  100- meters,  while  we  know  that 
the  rate  of  decrease  in  air  generally  in  the  summer  season, 
especially  in  the  lower  part  of  it,  is  much  greater,  and  conse- 
quently the  difference  of  temperature  above,  between  the 
ascending  air  and  the  surrounding  air  at  the  same  level,  must 
be  considerable. 

138.  During  the  month  of  April  the  weather  is  unsettled, 
and  the  wind  variable,  without  any  prevailing  direction.  By 
the  middle  of  May  the  summer  monsoon,  with  its  accompany- 
ing rains,  is  fairly  set  in,  and  soon  after  arrives  nearly  at  its  full 
strength.  The  general  direction  of  the  wind  on  the  Arabian 
Sea  is  from  the  southwest,  or  rather  from  the  west-southwest, 
and  is  here  called  the  Southwest  Monsoon.  The  direction  is 
more  from  the  west  than  it  otherwise  would  be,  both  on  account 
of  the  deflected  current  around  the  highlands  of  Asia,  §  123, 
and  also  on  account  of  the  deflecting  force  of  the  earth's  rota- 
tion, which,  however,  is  not  very  strong  here,  so  near  the 
equator.  Further  east,  in  the  Bay  of  Bengal,  the  wind  is  more 
southerly ;  along  the  coast  of  China,  and  over  the  Chinese  Sea, 
it  is  from  the  southeast,  and  in  Japan  it  is  still  more  easterly. 
Along  the  whole  of  the  north  coast  of  Siberia  the  wind  blows 
inland  during  the  summer  season,  though  not  directly  in  towards 
the  interior,  but  rather  from  the  northwest,  the  direction  being 
the  resultant  of  the  monsoon  influence  and  the  general  easterly 
tendency  of  the  atmosphere  in  these  latitudes.  The  prevailing 
direction  of  the  wind  observed  in  the  Vega  expedition  in 
summer  from  North  Cape  to  Yokohama  was  from  the  north- 
west. The  monsoon  influence  then  is  felt  on  the  north  side 
of  Asia  ;  but,  as  we  would  expect,  it  is  comparatively  weak, 
because  there  are  not  many  highlands  and  high  mountains  in 
Siberia,  and  the  effect  arising  from  the  condensation  of  aqueous 
vapor  is  small. 

The  general  tendency  in  the  summer  season  is  to  flow  in 
from  all  sides  toward  the  heated  interior,  with  a  slight  deflec- 


THE  MONSOONS  OF  ASIA   AND    THE  INDIAN   OCEAN.  20$. 

tion  to  the  right,  on  account  of  the  influence  of  the  earth's 
rotation,  and  consequently  to  flow  out  above  in  all  directions.. 
In  consequence,  however,  of  the  high  range  of  the  Himalayas, 
little  air  from  India  passes  over  this  range  toward  the  north  ;: 
but  it  continues  mostly  to  ascend  after  arriving  at  the  top  of 
the  slope,  until  it  is  immerged  into  the  returning  current  above 
toward  the  equator.  It  is  said,  however,  that  there  is  some  air 
passing  through  all  the  highest  passes  of  the  range,  on  toward 
the  interior  of  the  continent.  According  to  the  experience  of 
Prjivalsky  in  his  travels  over  the  high  plateau  of  Thibet  in 
June  and  July,  there  must  be  a  great  deal  of  air  brought  into- 
this  region  at  this  season,  which  in  ascending  gives  rise  ta 
much  rain.  It  is  said  :  "As  to  rain,  it  poured  down  every  day, — 
sometimes  several  days  without  interruption.  The  amount  of 
vapor  brought  by  the  southwest  monsoon,  and  deposited  there, 
is  so  great  that,  during  the  summer,  northern  Thibet  becomes 
an  immense  marsh."  But  this  vapor  comes  in,  most  probably,, 
from  other  directions,  and  not  from  the  southwest  monsoon 
only,  since  southern  Thibet,  next  the  Himalayan  range,  is. 
said  to  be  comparatively  dry. 

In  the  Arabian  Sea  the  monsoon  influence  in  summer  is  in 
the  right  direction  and  sufficiently  strong  to  entirely  overcome 
and  reverse  the  northeast  trade-wind ;  but  in  the  Chinese  Sea,, 
and  the  vicinity  of  the  Philippine  Islands,  the  effect  is  such  as 
to  change  the  northeast  trade-wind  to  a  southeast  wind.  Not 
only  is  the  regular  trade-wind  systems,  then,  of  the  North 
Indian  Ocean  entirely  broken  up  in  the  summer  season,  but 
the  monsoon  influence  draws  air  from  the  other  side  of  the 
equator,  thus  strengthening  the  southeast  trade-winds  there. 
This  is  especially  the  case  over  all  the  equatorial  region 
between  China  and  Australia,  since,  while  the  interior  of  Asia 
during  its  summer  is  heated  and  the  air  rarefied,  that  of  Aus- 
tralia is  cooled  and  its  pressure  increased,  so  that  the  tempera- 
ture and  pressure  gradients  between  the  two  countries  are  due 
to  both  causes.  There  is  consequently  no  equatorial  calm- 
belt  during  the  monsoon  ;  but  the  air  is  drawn  from  about  the 
parallel  of  25°  S.  across  the  equator  to  the  rarefied  central  part 


-204  MONSOONS,  AND  LAND-   AND   SEA-BREEZES. 

of  Asia — not  directly,  but  is  deflected  toward  the  west,  south  of 
the  equator,  and  then  eastward,  after  crossing  the  equator  to 
the  north  side,  by  the  deflecting  force  of  the  earth's  rotation. 
The  region  of  greatest  temperature,  or,  at  least,  of  greatest 
departure  from  the  normals  of  latitude,  upon  which  the  mon- 
soon depends,  and  lowest  barometric  pressure,  is  not  now  near 
the  equator,  but  in  the  interior  of  Asia,  and  the  highest  pres- 
.sure  is  in  the  southern  belt  of  high  pressure,  about  the  parallel 
of  30°  S.,  so  that  there  is  now  a  continuous  gradient  of  pressure 
•decreasing  from  this  belt  across  the  equator  into  the  interior  of 
-Asia.  There  is  therefore,  at  this  season  of  the  year,  an  enor- 
4nous  disturbing  influence,  due  to  this  monsoon,  which  entirely 
breaks  up  the  general  circulation  of  the  atmosphere  and  the 
"tropical  and  equatorial  calm-belts. 

139.  As  in  the  case  of  the  general  motions  of  the  atmos- 
phere, so  in  that  of  monsoons — wherever  the  vapor-laden 
current  strikes  a  range  of  hills  or  mountains,  and  is  deflected 
upward,  there  is  a  very  large  amount  of  rainfall  during  the 
•time.  The  current  of  the  southwest  monsoon,  in  its  passage 
from  the  Arabian  Sea  toward  the  southern  slopes  of  the 
Himalayas,  first  encounters  the  western  Ghauts,  a  range  of 
^mountains  from  4000  to  6000  feet  in  height,  near  the  Malabar 
coast,  where  a  great  part  of  its  vapor  is  condensed,  and  the 
rainfall  is  immense.  Passing  on  then  with  little  precipitation 
to  the  mighty  Himalayas,  it  now  in  the  ascent  loses  nearly  all 
of  the  remaining  part  of  its  vapor,  which,  falling  on  a  small 
area  on  account  of  the  steepness  of  the  slope,  causes  an 
immense  amount  of  rain  to  be  precipitated,  greater  or  less 
according  to  the  nature  of  the  country  and  the  height  and 
steepness  of  the  mountain  sides. 

But  the  greatest  rainfalls  are  experienced  in  the  mountains 
of  Khasia,  north  of  the  head  of  the  Bay  of  Bengal,  where  the 
warm  and  moist  air  of  the  nearly  equatorial  winds  blowing 
across  the  bay  is  somewhat  concentrated  by  the  converging 
•coasts  and  highlands  on  the  east  and  west  before  it  commences 
its  ascent  up  the  mountain  slopes,  and  having  previously  lost 
little  or  no  vapor  by  condensation,  as  it  does  in  the  case  of  the 


THE  MONSOONS  OF  ASIA   AND    THE  INDIAN  OCEAN. 

southwest  monsoon  in  passing  over  the  western  Ghauts,  the 
whole  vapor  is  now  condensed  in  the  ascent  of  the  Himalayan 
slope.  According  to  Dr.  Hooker,  as  cited  by  Laughton  : 18 

"  The  climate  of  Khasia  is  remarkable  for  its  excessive  rainfall.  At- 
tention was  first  drawn  to  it  by  Mr.  Yule,  who  stated  that  in  the  month 
of  August,  1841,  264  inches  fell,  or  twenty-two  feet;  and  that  during  five 
successive  days,  thirty  inches  fell  in  every  twenty-four  hours.  Dr.  Thom- 
son and  I  also  recorded  thirty  inches  in  one  day  and  night ;  and  during 
the  seven  months  of  our  stay  upward  of  500  inches  fell ;  so  that  the  total 
annual  rainfall  perhaps  greatly  exceeded  600  inches,  or  50  feet,  which  has- 
been  registered  in  succeeding  years.  From  April,  1849,  to  April,  1850,  502 
inches  fell.  This  unparalleled  amount  of  rainfall  is  attributable  to  the: 
abruptness  of  the  mountains  which  face  the  Bay  of  Bengal,  from  which 
they  are  separated  by  200  miles  of  Jheels  and  Sunderbunds." 

On  account  of  the  vast  amount  of  precipitation  during  the 
summer  monsoon  over  India,  and  especially  the  slopes  of  the 
Himalayas,  the  southwesterly  monsoon  of  the  Arabian  Sea  and 
western  India  and  the  more  southerly  monsoon  farther  east, 
is  often  called  the  Wet  Monsoon. 

140.  The  air  which  is  drawn  across  the  equator  during  the 
summer  monsoon  from  the  southern  hemisphere  of  course 
simply  strengthens  the  regular  southeast  trade-wind  which  ex- 
ists when  there  is  no  disturbance  from  the  monsoon  influence  ; 
but  at  and  a  little  north  of  the  equator  the  wind  becomes 
southerly,  and  still  farther  north  of  the  equator  it  is  deflected 
around  by  the  influence  of  the  earth's  rotation  into  a  north- 
easterly direction,  and  becomes  the  southwest  monsoon.  This 
is  clearly  shown  by  the  following  table  given  by  Woeikoff,33  of 
percentages  of  the  winds  from  the  different  directions  as  de- 
duced from  the  observations  on  the  ships  of  Holland,  during  the 
months  of  June,  July,  and  August  : 

Latitude.          E.  Long.          N.       N.E.       E.     S.E.       S.       S.W.      W.        N.W.       Cairns 
I0°— 15°  S.     80° —90° 
5  — 10  80  — 90 

o—5  75  —85 

o  —  5°  N.  80  —90 

5  — 10  80  — 90 

10—15  85—95 


I 

3 

17 

63 

12 

i 

i 

0 

2 

3 

9 

22 

40 

10 

8 

7 

2 

2 

i 

3 

22 

23 

15 

J2 

14 

5 

5 

i 

0 

0 

5 

18 

43 

24 

7 

2 

0 

i 

I 

3 

9 

57 

23 

2 

3 

0 

0 

0 

2 

10 

64 

13 

3 

9 

:206  MOiVSOOKS,  AND  LAND-   AND   SEA-BREEZES. 

From  this  table  it  is  seen  that  the  southeast  trade-wind 
gradually  changes  around  into  the  southwest  monsoon,  the  ob- 
served directions  being  mostly  southeasterly  south  of  the  equa- 
tor and  southwesterly  north  of  it,  and  there  is  apparently  no 
•calm-belt  at  or  near  the  equator. 

141.  Toward  the  end  of  October,  or  the  beginning  of  No- 
vember, the  interior  of  Asia  and  the  slopes  of  the  Himalayan 
range  are  cooled  down  to  the  mean  temperatures  of  the  year, 
.and  there  has  been  an  equalization  of  the  air-pressure,  and  the 
monsoon  has  subsided  ;  or  rather,  the  pressures  have  changed 
to  the  normal  pressures  for  the  mean  temperature  of  the  year, 
and  the  winds  to  those  of  the  corresponding  general  circula- 
tion, with  high  pressure  and  calms  near  the  two  tropics,  and 
low  pressure  and  calms  near  the  equator.  But  now  a  reversion 
of  the  summer  conditions  gradually  takes  place.  During  the 
winter  season  of  the  northern  hemisphere  the  interior  of  Asia, 
and  especially  of  Siberia,  becomes  cooled  down  by  the  radia- 
tion of  heat  into  space,  through  the  now  very  dry  air,  to  a  very 
low  temperature,  far  below  that  of  the  normals  of  latitude  for 
the  season,  and  the  density  of  the  air  and  the  barometric  pres- 
sure are  very  much  increased,  instead  of  being  diminished  as  in 
the  summer  season.  The  effect  is  now  a  complete  reversal  of 
all  the  motions  between  the  central  and  surrounding  regions, 
and  instead  of  a  flowing  in  below  from  all  sides  toward  the  cen- 
tral part,  and  a  flowing  out  above  in  all  directions,  the  flow  is 
outward  below  and  inward  above.  The  southern  slope  of  the 
Himalayas  is  now  cooled  by  radiation  far  below  the  general 
temperature  of  the  air  at  the  same  levels  at  a  distance  from  it, 
•and  the  stratum  of  air  in  contact  becomes  dense  and  heavy,  and 
consequently  tends  to  flow  down  toward  the  lower  levels  of 
India  and  the  Indian  Ocean.  The  monsoon  is  now  completely 
reversed,  and  instead  of  S.W.,  S.,  and  S.E.  winds  around  the 
southern  and  eastern  coasts  of  Asia,  there  are  N.E.,  N.,  and 
N.W.  winds. 

The  wind  over  the  Arabian  Sea  and  India  depending  upon 
the  monsoon  influence  being  mostly  a  northeast  wind  combines 
with  the  regular  trade-winds  of  these  latitudes,  and  the  result- 


THE  MONSOONS   OF  ASIA   AND    THE  INDIAN  OCEAN.  2O/ 

ant  is  a  stronger  wind  than  that  which  would  arise  from  the 
monsoon  influence  alone,  but  still  not  nearly  so  strong  as  that 
of  the  southwest  monsoon.  It  is  called  the  Northeast  Monsoon, 
and  the  monsoons  generally  of  the  winter  season  of  the  region 
south  and  east  of  Asia  are  often  called  the  Winter  Monsoons. 
Since  the  air  of  these  monsoons  comes  from  the  elevated  dry 
and  cool  interior  of  the  continent  into  warmer  regions  of  lower 
level,  it  is  very  dry,  especially  that  in  India  which  comes  down 
from  the  Himalayas.  Hence  these  monsoons  are  often  called 
the  Dry  Monsoons. 

But  when  the  northeasterly  monsoon  does  not  come  di- 
rectly from  the  elevated  and  dry  interior  of  the  continent,  but 
blows  a  long  distance  over  the  sea,  on  coming  in  contact  with 
mountain  ranges,  as  in  Ceylon,  it  gives  rise  to  just  as  much 
rain,  or  nearly  so,  as  the  southwest  monsoon.  The  latter  is 
usually  a  little  the  stronger,  and  blowing  from  more  southern 
latitudes  may  have  a  little  more  vapor,  and  so  for  both  reasons 
give  rise  to  a  little  more  rain. 

In  the  summer  or  wet  monsoons  we  have  the  effect  of  the 
latent  heat  of  condensation  in  connection  with  that  of  the 
heating  from  the  sun's  radiation,  but  in  the  winter  and  dry 
monsoons  we  have  simply  the  effect  from  greater  cooling  by 
radiation,  which  is  about  equivalent  only  to  that  from  the 
greater  heating  in  summer  from  solar  radiation,  so  that  the 
effect  is  not  nearly  so  great  in  the  case  of  the  winter  monsoons 
as  in  that  of  the  summer  monsoons  in  which  much  energy 
arises  from  the  latent  heat  of  condensation  of  aqueous  vapor. 
Accordingly  the  northeast  monsoon,  though  strengthened  by 
the  regular  northeast  trade-wind,  is  not  nearly  so  strong  as  the 
southwest  monsoon,  as  has  been  already  stated  in  §  136. 

During  the  winter  season  the  winds  of  Northern  Siberia, 
especially  near  the  coast,  are  mostly  southerly,  blowing  from 
the  colder  continent  toward  the  warmer  polar  sea,  and  hence  in 
a  direction  nearly  the  reverse  of  that  of  the  polar  winds  of  the 
summer  season.  There  is,  therefore,  a  monsoon  along  this 
coast  with  alternating  winds  of  no  great  strength  ;  but  these 
are  not  exactly  opposite  in  direction,  but  rather  from  the 


208  MONSOONS,  AND  LAND-  AND   SEA-BREEZES. 

northwest  in  summer  and  the  southwest  in  winter,  owing  to  the- 
general  prevalence  of  westerly  winds  in  these  latitudes  arising 
from  the  general  circulation  of  the  atmosphere. 

"  In  winter  the  whole  coast  of  Norway  has  monsoon  winds,  blowing 
from  the  land  to  the  sea:  they  are  N.  and  N.E.  at  Christiania ;  S.E.  at 
Christiansund,  Bosekop,  and  Hammerfest ;  and  S.W.  at  Vardoe.  In  sum- 
mer the  conditions  are  reversed.  In  northern  Norway  the  winds  are 
variable  in  summer,  and  decidedly  from  the  S.  in  winter."  20 

142.  On  account  of  the  great  lowering  of  temperature  in 
Asia  in  winter  below  that  of  the  normals  of  latitude,  which, 
considered  alone,  gives  rise  in  the  general  circulation  to  a  belt 
of  high  pressure  about  the  parallel  of  35°,  and  one  of  low  pres- 
sure at  or  near  the  equator,  this  regular  system  is  now  com- 
pletely broken  up,  and  the  highest  pressure  is  found  in  the  in- 
terior of  Asia,  and  there  is  a  gradient  of  decreasing  pressure 
thence  to  about  the  parallel  of  12°  south  of  the  equator  in  the 
Indian  Ocean.  The  normal  equatorial  belt  of  low  pressure  and 
calms  is  now  transferred  to  this  parallel,  where  the  northerly 
monsoon  of  Asia,  crossing  the  equator,  meets  the  regular 
southeast  trade-winds,  and  hence  the  belt  of  these  trade-winds 
is  now  confined  within  the  limits  of  the  parallels  of  12°  and 
about  25°  or  30°  S.  After  the  northeasterly  and  northerly 
winds  of  the  winter  monsoon  pass  over  the  equator  they  are 
deflected  to  the  east  by  the  force  depending  upon  the  earth's 
rotation,  which  is  towards  the  left  in  this  hemisphere,  so  that 
there  is  a  belt  between  the  equator  and  the  parallel  of  12°  S., 
where  the  prevailing  direction  of  the  wind  is  from  the  north- 
west. This  is  called  the  Northwest  Monsoon.  Where  this 
monsoon  meets  the  southeast  trade-winds  we  have  the  condi- 
tions of  the  equatorial  calm-belt,  a  meeting  of  counter  currents,, 
calms,  an  ascending  current  over  a  belt  of  several  degrees  in 
width,  and  consequently  an  abundance  of  condensation  and  of 
rainfall  over  this  belt.  Espy  says  : 34  "  The  monsoon  in  the 
Indian  Ocean,  which  blows  from  the  northwest  during  the  sum- 
mer, terminates  in  a  belt  of  rains  6000  miles  long." 

On  the  western  side  of  the  southern  Indian  Ocean  the  north- 
west monsoon  is  much  modified  by  the  whirl  of  atmosphere 


THE  MONSOONS  OF  ASIA   AND    THE  INDIAN  OCEAN.  2(X) 

deflected  by  the  high  table-lands  and  mountain  ranges  of  the 
east  coast  of  Africa,  §  125,  by  which  the  direction  of  the  wind 
is  changed  and  the  monsoon  is  changed  to  what  is  called  in 
this  region  the  Northern  Monsoon.  According  to  Espy,  "  the 
northern  monsoon,  which  blows  into  the  northern  end  of  the 
Mozambique  Channel  in  the  southern  summer,  terminates 
there  in  a  great  rain,  and  the  southern  trade,  which  blows  into 
the  same  channel  at  the  same  time,  terminates  there  in  the 
same  rain ;  and  the  ship  that  is  caught  in  that  channel  at  that 
season  finds  the  wind  dead  against  her  at  whichever  end  of  it 
she  tries  to  escape."  This  rainy  portion  of  the  channel  at  this, 
time  is  simply  the  western  end  of  the  general  rainy  belt  of  the 
Indian  Ocean  explained  above  and  referred  to  by  Espy,  but 
moved  here  a  little  farther  south  than  it  is  farther  east,  by 
the  atmospheric  whirl  referred  to  above. 

143.  There  are  monsoon  influences  arising  from  the  annual 
alternations  of  temperature  in  Australia  similar  to  those  of 
Asia,  but  on  account  of  its  smaller  extent  and  the  absence  of 
very  high  plateaus  and  mountain  ranges,  these  influences  are 
comparatively  small.  In  Asia  the  monsoon  influence,  at  least 
at  the  extremes,  is  the  predominating  one,  giving  rise  to  at- 
mospheric disturbances  and  velocities  of  air  currents  by  far 
greater  than  those  of  the  general  circulation  of  the  atmos- 
phere, so  that  the  latter  merely  cause  perturbations  in  the 
regular  annual  alternations  and  inversions  of  the  monsoon.. 
In  the  case  of  Australia,  however,  the  monsoon  influence  is  the 
weaker,  and  its  effects  merely  cause  perturbations  in  the  gen- 
eral circulation  of  the  atmosphere.  The  continent  lying  mostly 
within  the  belt  of  the  southeast  trade-winds,  these  in  its  vicin- 
ity are  considerably  modified  all  around  the  coast  of  the  north- 
ern half  of  it,  and  also  the  prevailing  westerly  winds  in  the 
region  on,  and  adjacent  to,  the  southern  coast. 

During  the  summer  of  the  southern  hemisphere,  when  the 
earth  is  in  perihelion,  the  whole  land,  exposed  to  an  almost 
vertical  sun  at  midday,  and  lying  mostly  in  the  southern  zone 
of  high  pressure  and  dry  air  (§  120),  becomes  intensely  heated, 
far  above  the  temperature  of  the  surrounding  ocean.  Conse- 


2IO  MONSOONS,  AND  LAND-   AND   SEA-BREEZES. 

quently  the  tendency  now  is  for  the  air  below  to  flow  in  from 
all  sides  toward  the  central  part,  and  of  course  the  contrary 
above.  In  this  flow,  however,  the  currents  are  deflected  a  lit- 
tle to  the  left  by  the  force  depending  upon  the  earth's  rotation, 
but  this  force  is  small  on  the  northern  side  on  account  of  its 
nearness  to  the  equator.  On  the  northeast  side  of  Australia, 
where  the  southeast  trade-winds  prevail,  their  directions  are 
now  changed,  so  that  they  become  easterly  and  northeasterly 
winds,  especially  during  the  day.  On  the  eastern  side  along 
the  coast  of  New  South  Wales,  which  is  in  the  south  tropical 
calm-belt,  where  calms  prevail  when  there  is  no  monsoon  or 
other  abnormal  atmospheric  disturbance,  the  wind  blows  from 
the  ocean  toward  the  interior  of  the  continent.  Along  the 
southern  and  southwestern  coast  the  westerly  and  northwest- 
erly winds  which  prevail  in  these  latitudes  are  a  little  changed 
in  direction  by  the  monsoon  influence  and  blow  from  a  more 
southerly  direction.  On  the  northwest  coast,  in  the  zone  of 
the  regular  southeast  trade-winds,  the  monsoon  influence  is  not 
strong  enough  to  reverse  them,  even  in  midsummer,  so  that 
here  the  wind  at  all  seasons  blows  from  the  land  toward  the 
ocean,  but  with  a  strength  a  little  diminished  by  the  monsoon 
influence.  The  effect  of  this  is  to  bring  the  line  of  meeting 
between  the  northwest  monsoon  and  the  southeast  trade-winds 
a  little  farther  south  than  it  is  over  the  South  Indian  Ocean 
generally,  where  this  monsoon  influence  is  not  felt,  so  that  in 
the  ocean  adjacent  to  the  north  and  northwest  coast  this  line 
is  brought  down  several  degrees  south  of  the  parallel  of  12°,  and 
passes  over  the  northern  extremity  of  the  continent. 

144.  The  climatic  effect  of  the  summer  monsoon  influence 
in  Australia,  where  it  is  not  counteracted  by  the  regular  south- 
east trade-winds,  is  to  bring  in  cool  and  moist  air  from  the 
cooler  ocean  into  the  dry  and  heated  interior,  and  so  to  modify 
the  intense  heat  along  the  coast  and  to  increase  the  rainfall. 
Accordingly  on  all  sides  from  the  north  around  by  east  to  the 
southwest  side,  where  the  wind  blows  from  the  ocean  inland, 
there  is  an  abundance  of  rainfall,  as  may  be  seen  from  Loomis's 
chart.22  But  for  this  influence,  along  the  coast  of  New  South 


THE  MONSOONS  OF  ASIA   AND    THE  INDIAN  OCEAN.  211 

"Wales,  where  otherwise  calms  would  prevail,  there  would  be 
the  same  scant  rainfall,  or  nearly  so,  as  in  the  interior  on  the 
same  latitudes.  This  rainfall  all  along  the  eastern  side  is  much 
increased,  though  reduced  to  a  much  narrower  strip,  by  the 
succession  of  mountain  ranges  from  3000  to  5000  feet  high 
near  the  coast. 

The  abundance  of  rain  on  the  northern  extremity  of  Aus- 
tralia in  summer  is -due  to  the  line  of  the  meeting  of  the  south- 
east trade-winds  with  the  northwest  monsoon,  and  the  conse- 
quent accompanying  rain-belt,  passing  over  it  at  this  season ; 
for  it  is  simply  the  normal  equatorial  rain-belt  brought  down 
to  this  parallel,  mostly  by  the  Asiatic  monsoon  influence,  but 
jin  part  also  by  that  of  Australia,  as  has  been  explained  above. 

Along  the  west  and  northwest  coast  of  Australia  there  is 
little  rain,  because  here  the  regular  southeast  trade-winds  pre- 
vail at  all  seasons,  bearing  away  the  warm  and  dry  air  of  the 
interior  toward  the  ocean;  for  if  there  were  even  mountain 
ranges  here  to  cause  -upward  deflections,  the  amount  of  moist- 
ure in  the  air  coming  from  the  interior  of  the  continent  would 
be  too  scant  to  give  .rise  to  much  rain. 

145.  During  the  winter  of  the  southern  hemisphere  the 
conditions  are  mostly  reversed,  and  there  is  now  a  tendency  of 
the  air  to  flow  out  below  in  all  directions  from  the  interior 
"toward  the  ocean.  The  effect  of  this  along  the  northeast  coast, 
where  the  southeasterly  trade-winds  blow,  is  to  change  them 
somewhat  to  more  southerly  winds,  which  are  found  to  prevail 
here  at  this  season.  Further  south,  however,  along  the  coast 
of  New  South  Wales,  in  the  belt  of  calms  and  high  pressure, 
and  where  easterly  winds  prevail  in  summer,  there  are  now 
westerly  winds,  so  that  here  there  is  a  somewhat  regular  mon- 
soon, but  of  no  great  strength.  The  monsoon  effect  upon  the 
prevailing  westerly  winds  along  the  south  and  southwest  coast 
is  to  cause  them  to  blow  from  a  direction  a  little  more  from 
the  northwest.  Along  the  whole  of  the  northwest  coast  and 
'Over  the  whole  northern  half  of  the  continent  there  are,  at  this 
season,  the  regular  southeast  trade-winds,  but  strengthened 
somewhat  by  the  monsoon  influence. 


212  MONSOONS,  AND  LAND-   AND    SEA-BREEZES. 

The  climatic  effect  of  the  winter  monsoon  influence  is  to 
increase  the  dryness  and  to  diminish  the  amount  of  rainfall 
over  the  whole  of  the  interior,  which,  aside  from  this  influence, 
is  a  very  dry  region,  from  its  lying  mostly  in  the  south  tropical 
zone  of  high  pressure  and  in  the  zone  of  the  trade-winds,  in) 
both  of  which  there  is,  in  general,  little  rainfall. 

Since  the  mean  temperature  of  land  in  tropical  and  equa- 
torial latitudes,  for  reasons  given  in  §  68,  is  greater  than  that  of 
the  ocean  on  the  same  latitudes,  the  strength  of  the  winter 
monsoon  influence  is  less  than  that  of  the  summer.  For  if  we 
suppose  that,  in  the  annual  oscillation  of  temperature,  this  rises 
in  summer  as  far  above  the  mean  annual  temperature  as  it  falls 
below  in  winter,  then  the  difference  between  the  land  temper- 
ature and  that  of  the  ocean  must  be  greater  in  summer  than  in 
winter,  since  the  mean  temperature  of  the  land  is  higher  than 
that  of  the  ocean,  and  hence  the  air-pressure  is  decreased  more 
below  the  annual  mean  of  the  ocean  during  the  Australian.! 
summer  than  it  is  raised  above  it  in  winter. 

THE   MONSOONS   OF  AFRICA. 

146.  For  reasons  given  in  the  case  of  Australia,  the  mean  an- 
nual temperature  of  the  whole  of  equatorial  and  tropical  Africa. 
is  higher  than  that  of  the  oceans  on  the  same  latitudes.  Since- 
the  monsoon  influence  depends  upon  the  range  of  the  annual 
oscillation  of  temperature,  and  this  is  not  very  great  here,  so 
near  the  equator,  this  influence  is  not  so  great  here  as  it  other- 
wise would  be:  in  fact,  there  is  little  of  the  real  monsoon  influ- 
ence, which  would  cause  a  reversion  of  directions  at  the  two 
seasons  ;  for  the  mean  temperature  of  the  land  being  consider- 
ably greater  than  that  of  the  ocean,  it  scarcely  becomes  lower 
in  general  than  that  of  the  ocean  in  winter..  The  consequence 
is,  that  while  there  is  a  strong  tendency  in  the  air  at  the  earth's-, 
surface  to  flow  in  from  the  ocean  in  summer,  or  at  the  times  of 
highest  temperature,  there  is  little  or  no  tendency  to  flow  outr 
when  the  temperature  of  the  land  is  reduced  to  the  lowest, 
since  it  is  then  but  little  below  the  temperature  of  the  adjacent. 


THE  MONSOONS  OF  AFRICA. 

ocean.  Over  the  whole  of  the  northern  part  of  Africa,  and 
even  over  the  Mediterranean  Sea,  the  regular  northeast  trade- 
wind  prevails,  with  slight  annual  variations  and  strengthened  a 
little  by  the  summer  monsoon  influence,  throughout  the  whole 
year ;  but  along  the  northwest  coast  of  Africa,  and  to  a  con- 
siderable distance  over  the  adjacent  part  of  the  Atlantic,  it 
becomes  northerly  and  even  northwesterly  in  midsummer,  the 
air  being  drawn  in  towards  the  heated  region  of  the  Sahara. 
At  the  same  time  in  the  Gulf  of  Guinea  and  to  some  distance 
into  the  Atlantic,  the  regular  southeast  trade-wind  is  changed, 
first  to  a  southerly,  and  nearer  the  coast  to  a  southwesterly 
wind,  called  the  Southwest  Monsoon  of  Africa,  which  is  really 
not  a  monsoon,  but  simply  a  change  in  direction  of  the  regular 
trade-winds  by  the  indraught  of  air  toward  the  Sahara  at  this 
season.  But  at  the  opposite  season  there  is  little  reversing 
action,  since  there  is  then  but  little  difference  between  the  tem- 
perature of  the  land  and  that  of  the  ocean,  and  so  the  south- 
east trade-wind  then  has  nearly  its  usual  direction. 

147.  West  of  the  Gulf  of  Guinea  and  the  coast  of  Liberia, 
•and  a  little  north  of  the  equator,  there  is  a  wedge-shaped  area 
with  its  apex  extending  far  west  into  the  Atlantic  Ocean,  in 
which  calms  and  light  variable  winds  usually  prevail,  and  the 
^vvinds,  especially  in  the  summer  season  of  the  northern  hemi- 
sphere, sometimes  blow  directly  in  toward  the  interior  of  Africa. 
This  is  caused  by  the  nearly  permanent  difference  of  temper- 
ature between  the  equatorial  parts  of  the  continent  and  the 
ocean ;  for  the  annual  variations  here  are  small,  and  conse- 
quently there  is  very  little  real  monsoon  effect,  or  reversal  of 
the  winds  with  the  seasons.  The  tendency  is  to  draw  the  air 
in  from  the  ocean  toward  the  Sahara,  and  this  entirely  counter- 
acts the  regular  northeasterly  trade-winds  in  summer  up  to  the 
parallel  of  about  13°,  causing  an  apparent  widening  of  the  equa- 
torial calm-belt  in  this  region.  During  the  winter  of  the  north- 
ern hemisphere,  when  the  Sahara  becomes  cooled  down  some- 
what and  the  region  of  greatest  heat  and  rarefaction  of  the  air 
is  transferred  to  South  Africa,  the  northeasterly  trade-winds 
jblow  again  to  a  lower  latitude,  as  in  other  parts,  and  there  is 


214  MONSOONS,  AND  LAND-   AND   SEA-BREEZES. 

now  a  considerable  narrowing  of  this  area.  The  tendency  now 
is  to  draw  the  air  more  toward  South  Africa,  so  that  this  area, 
not  only  becomes  narrower,  but  there  is  now  often  a  northwest- 
erly wind  blowing  from  this  region  into  the  Gulf  of  Guinea. 

There  is  a  wide  zone  through  Central  Africa,  comprising 
the  country  of  the  Soudan,  and  lying  mostly  between  the  paral- 
lels of  5°  and  15°  N.  and  extending  eastward  to  the  Abyssinian 
mountains,  in  which  there  is  apparently  a  somewhat  regular- 
monsoon,  the  winds  changing  with  the  seasons  from  a  north- 
easterly or  northerly  direction  in  the  winter  to  a  southerly  di- 
rection in  the  summer.  During  the  winter  the  regular  trade- 
winds,  which  are  always  more  northerly  on  land,  where  there  is 
more  friction,  than  on  the  ocean,  where  there  is  less,  blow  down 
to  the  parallel  of  about  5°  N.  But  during  the  summer  the 
southeasterly  trade-winds,  becoming  southerly  winds  at  and 
near  the  equator  on  account  of  there  being  here  no  deflecting 
force  from  the  earth's  rotation,  blow  up  to  about  the  parallel 
of  15°  N.,  and  hence  between  these  parallels  there  is  an  annual 
reversion  of  the  directions  of  the  winds  from  northerly  winds, 
or  nearly  so,  in  the  winter,  to  southerly  winds  in  the  summer,, 
of  the  northern  hemisphere,  and  back  again.  This,  however, 
arises  mostly  from  the  general  oscillation  of  the  equatorial' 
calm-belt  all  around  the  globe,  depending  upon  varying  tem- 
perature conditions  extending  over  the  whole  of  each  hemi- 
sphere, as  has  been  explained,  but  also  in  some  measure  upon 
the  annual  transfer  of  the  local  more  heated  regions  of  Africa 
from  the  northern  to  the  southern  hemisphere  and  back  again. 
The  same  is  observed  more  or  less  in  nearly  all  parts  of  the 
zone  over  which  the  equatorial  calm  and  rain-belt  oscillates. 

MONSOONS   OF   NORTH   AMERICA. 

148.  On  the  continent  of  North  America  we  have  monsoon 
influences  similar  to  those  of  Asia,  but  not  nearly  so  strong,, 
because  the  extent  of  the  continent,  and  consequently  the  an- 
nual range  of  temperature,  are  not  so  great.  They  are,  for  the 
most  part,  not  sufficiently  strong  to  completely  overcome  and! 


MONSOONS  OF  NORTH  AMERICA.  21$ 

reverse  the  current  of  the  general  circulation  of  the  atmosphere, 
and  so  to  produce  a  real  monsoon,  but  they  cause  great  differ- 
ences between  the  prevailing  directions  of  the  winter  and  sum- 
mer winds. 

In  the  summer  the  whole  interior  of  the  continent  becomes 
heated  up  to  .a  temperature  much  above  that  of  the  oceans  on 
the  same  latitudes  on  each  side — indeed  above  that  of  the  Gulf 
of  Mexico  and  the  Pacific  Ocean  on  its  southern  and  southwest- 
ern borders.  The  consequence  is  that  the  air  over  the  interior 
of  the  continent  becomes  more  rare  than  over  the  oceans,  rises 
up,  and  flows  out  in  all  directions  above  while  the  barometric 
pressure  is  diminished,  and  the  air  from  all  sides,  from  the 
Atlantic  on  the  east,  the  Pacific  Ocean  on  the  west,  the  Gulf  of 
Mexico  on  the  south,  and  the  polar  sea  on  the  north,  flows  in 
below  to  supply  its  place.  On  the  east  the  tendency  to  flow  in 
is  not  strong  enough  to  counteract  the  general  easterly  motion 
of  the  air  at  the  earth's  surface  in  the  middle  latitudes,  and  to 
cause  a  westerly  current,  but  it  simply  retards  the  general  east- 
erly current  and  gives  rise  to  a  greater  prevalence  of  easterly 
winds  along  the  Atlantic  sea-coast  during  the  summer  season. 
On  the  southern  and  southeastern  coast,  in  connection  with 
the  deflection  referred  to  in  §  123,  it  causes  the  prevailing  winds 
to  be  southerly  and  southeasterly  instead  of  northeasterly, 
as  they  otherwise  would  be  in  these  trade-wind  latitudes. 
It  is  precisely  the  same  effect  as  is  produced  in  the  region 
southeast  of  China  (§  138).  The  monsoon  influence  in  the 
Mississippi  valley  and  westward  is  much  strengthened  by  the 
gradual  slope  from  this  valley  up  to  the  high  plateaus  east  of 
the  Rocky  Mountain  range,  for  reasons  which  have  been  al- 
ready given  (§  132);  so  that  when  this  slope  in  summer  be- 
comes heated  the  surface  air  tends  to  flow  up  it  toward  the 
mountain  range,  and  causes  winds,  which  otherwise  would  be 
southerly  ones,  to  become  more  southeasterly,  and  southwest- 
erly winds  to  become  southerly  ones. 

In  winter  the  thermal  conditions  over  the  continent  are 
reversed.  The  interior  of  the  continent  is  now  the  coldest 
part,  and  it  is  especially  colder  than  the  surrounding  oceans  at 


2l6  MONSOONS,  AND  LAND-   AND   SEA-BREEZES. 

that  season.  It  has  also  very  high  plateaus  and  mountain 
ranges.  The  air,  therefore,  of  the  lower  strata,  and  especially 
those  next  the  earth's  surface,  now  tends  to  flow  out  in  all 
directions  to  the  warmer  oceans  and  the  Gulf  of  Mexico,  and 
especially  to  run  down  the  long  slope  of  plateau  from  the 
Rocky  Mountains  into  the  Mississippi  valley.  The  effect  over 
the  whole  of  the  United  States  east  of  the  Rocky  Mountains 
is  to  cause  the  winds,  which  otherwise  would  be  westerly 
and  southwesterly,  to  become  generally  northwesterly  winds, 
instead  of  southerly  and  southwesterly  ones,  as  in  summer. 
There  is  not  a  complete  monsoon  effect,  but  simply  a  great 
change  between  summer  and  winter  in  the  prevailing  direc- 
tions of  the  winds.  In  Texas,  however,  and  farther  east  along 
the  northern  border  of  the  Gulf,  the  effect  is  somewhat  that  of 
a  complete  monsoon.  In  New  England  and  farther  south  in 
the  Eastern  States  the  monsoon  effect  is  to  cause  the  prevail- 
ing winds  to  be  from  some  point  north  of  west,  instead  of  souch 
of  west  as  in  summer. 

149.  In  summer  Central  America  and  Mexico  have  a  much 
higher  temperature  than  that  of  the  adjacent  tropical  sea  on 
the  southwest,  and  having  high  mountain  ranges  and  elevated 
plateaus,  there  is  consequently  a  strong  tendency  to  draw  in 
air  from  the  southwest  at  this  season,  which  not  only  entirely 
counteracts  the  regular  trade-winds  of  these  latitudes,  but  even 
reverses  them  and  causes  southwest  winds.  The  effect  is  to 
cause  in  midsummer  a  large  area  here,  extending  far  westward, 
of  calms  and  irregular  and  light  winds,  mostly  southwesterly 
ones,  and  an  apparent  widening  of  the  equatorial  calm-belt  at 
this  season  so  as  to  make  its  northern  limit  reach  up,  along  the 
coast,  nearly  to  the  parallel  of  20°.  The  effect  is  similar  to 
that  in  the  Atlantic  west  of  the  Gulf  of  Guinea  and  Liberia, 
except  that  it  here  appears  to  be  some  greater,  and  causes  a 
true  monsoon  effect,  since  during  the  winter  the  regular  north- 
easterly trade-winds  prevail,  but  strengthened  by  the  reverse 
thermal  conditions  of  the  winter  season.  On  the  eastern  side 
and  over  the  western  end  of  the  Gulf  of  Mexico  there  is  a 
somewhat  regular  monsoon  effect,  the  prevailing  winds  being 


MONSOONS  OF  SOUTH  AMERICA.  2 1/ 

-easterly,  or  blowing  toward  the  land,  during  the  summer,  and 
the  reverse  in  winter. 

Along  the  west  coast  of  North  America  in  the  middle  lati- 
tudes there  is  a  strong  monsoon  influence ;  for  the  interior  of 
the  continent  becomes  heated  in  summer  to  a  much  higher 
temperature  than  that  of  the  southwesterly  ocean,  and  hence  a 
strong  current  is  drawn  in  from  this  direction,  at  right  angles 
to  the  general  trend  of  the  coast,  which,  combining  with  the 
general  southwesterly  winds  of  these  latitudes  in  the  general 
circulation  of  the  atmosphere,  causes  the  strong  and  steady 
westerly  and  southwesterly  winds  of  this  region  during  the 
summer.  Farther  north,  up  toward  Alaska,  the  summer  mon- 
soon effect  is  combined  with  the  current  caused  by  the  deflec- 
tion of  the  continent  (§  123)  as  well  as  the  general  easterly  cur- 
rent of  high  latitudes,  so  that  the  winds  here  are  generally 
southerly,  but  still  have  somewhat  of  a  monsoon  character, 
being  southerly  and  southwesterly  in  summer,  and  easterly  and 
southeasterly  during  the  winter. 

All  along  the  northern  coast  of  America,  as  along  that  of 
Siberia,  the  monsoon  tendency  is  to  draw  the  air  from  the 
colder  land  to  the  warmer  ocean  in  winter,  and  the  reverse  in 
summer ;  and  these  effects,  combined  with  the  general  easterly 
motion  of  the  atmosphere  in  these  latitudes,  gives  rise  to  pre- 
vailing southwesterly  winds  in  winter  and  northwesterly  ones 
in  summer.  The  winter  monsoon  influence,  however,  is  small 
here — much  more  so  than  in  Siberia,  for  the  ocean  contains  so 
many  large  islands  that  it  has  rather  a  continental  than  an 
oceanic  winter  temperature ;  and  besides,  it  has  not  the  influ- 
ence of  a  warm  current — such  as  the  continuation  of  a  part  of 
the  Gulf  Stream  along  the  northern  coast  of  Europe  and  Asia. 

MONSOONS   OF  SOUTH  AMERICA. 

150.  In  South  America  we  have  conditions  similar  to  those 
of  Australia,  and  the  monsoon  influences  are  well  marked,  being 
stronger  than  those  of  Australia,  both  because  the  continent  is 
larger  and  the  mountain  ranges  higher.  Along  the  northeast- 


2l8  MONSOONS,  AND   LAND-   AND   SEA-BREEZES. 

ern  coast  of  South  America,  and  in  the  whole  Amazon  valley,, 
the  indraught  of  air  from  the  ocean  toward  the  interior  of  the  con- 
tinent and  the  eastern  slope  of  the  Andes  is  so  strong  during 
the  summer  of  the  southern  hemisphere,  that  there  is  now  a 
continuous  northeasterly  wind  from  the  region  of  the  north- 
easterly trade-winds,  far  into  the  interior,  and  the  monsoon 
effect  appears  as  a  continuation  of  these  trade-winds  across  the 
equator  into  the  opposite  hemisphere.  But  this  is  somewhat 
of  a  perennial  effect,  though  much  greater  during  the  summer 
of  the  southern  hemisphere  than  at  the  opposite  season.  For 
the  mean  temperature  of  equatorial  and  tropical  South  Amer- 
ica being  considerably  greater  than  that  of  the  oceans,  and  the 
annual  thermal  changes  being  small,  there  is  perhaps  scarcely 
any  time  when  the  land  is  colder  than  the  ocean,  and  when 
there  is  a  reverse  monsoon  effect. 

The  effect  of  the  monsoon  influence  in  summer  over  Brazil,, 
which  is  mostly  in  the  zone  of  the  southeasterly  trade-winds,, 
together  with  that  of  the  deflection  by  the  continent,  and  espe- 
cially the  range  of  the  Andes,  is  to  change  these  winds  into 
northeasterly  and  northerly  ones,  which  are  the  prevailing 
winds  here  in  the  summer.  The  effect  is  similar  to  that  in  the 
southern  part  of  the  United  States  and  the  Gulf  of  Mexico,  by 
which  the  winds  here  are  changed  from  the  regular  northeast- 
erly trade-winds  to  southeasterly  and  southerly  winds  in  the 
summer  season.  During  the  winter  the  winds  are  more  vari- 
able here,  since  the  monsoon  influence  rather  antagonizes  the 
easterly  and  northerly  winds  which  arise  from  the  deflection 
of  the  continent  and  the  Andes,  but  they  are  largely  polar 
and  southwesterly  winds,  as  in  the  corresponding  part  of  the 
United  States  they  are  polar  and  northwesterly  winds. 

On  the  coast  of  Chili  and  the  adjacent  part  of  the  ocean 
the  prevailing  winds  are  mostly  southerly  and  southwesterly  in 
December,  January,  and  February,  the  southern  summer,  but 
northerly  and  northwesterly  at  the  opposite  season  of  the  year. 
This  arises  in  part  from  the  deflection  of  the  strong  westerly 
winds  of  these  latitudes  by  the  lofty  range  of  the  Andes,  and 
in  part  from  the  monsoon  effect,  by  which  the  air  is  drawn  ia 


LAND-  AND   SEA-BREEZES.  2IC/ 

toward  the  interior  of  the  continent,  and  by  which  they  are 
strengthened  but  not  much  changed  in  direction.  At  the  op- 
posite season  of  the  year  this  monsoon  influence  is  in  the  con- 
trary direction,  and  reverses  the  directions,  giving  rise  to  north- 
erly and  northeasterly  winds,  but  of  less  strength. 

Farther  south  toward  the  Cape  northwesterly  winds  prevail 
the  whole  year,  arising  in  part  from  the  deflection  of  the  pre- 
vailing westerly  winds  of  the  middle  latitudes  by  the  Andes 
toward  the  south.  The  monsoon  influence  is  also  here  per- 
ceptible in  causing  these  winds  to  be  more  northerly  in  winter 
than  in  summer. 

Along  the  coast  of  Peru  and  on  the  adjacent  ocean,  in  the: 
latitudes  of  the  southeasterly  trade-winds,  the  temperature  of 
the  continent  being  greater  than  that  of  the  oceans,  there  is  a 
tendency  of  the  air  the  whole  year  to  flow  in  toward  the  land, 
but  especially  in  December,  January,  and  February,  which, 
however,  is  not  strong  enough  to  change  the  direction,  even  at 
this  season,  of  the  southeasterly  trade-winds  so  much  as  to 
make  them  southwesterly  winds,  as  in  the  Gulf  of  Guinea,  but 
it  simply  makes  them  a  little  more  southerly  than  they  other- 
wise would  be. 

LAND-  AND   SEA-BREEZES. 

151.  Land-  and  sea-breezes  are  observed  in  all  countries 
wherever  there  is  a  diurnal  alternation  of  the  temperature  of 
the  land,  above  that  of  the  adjacent  ocean  during  the  day,  and 
below  it  during  the  night — just  as  there  are  monsoons  where 
this  temperature  over  a  whole  continent  or  large  area  of  coun- 
try is  higher  than  that  of  the  oceans  or  surrounding  parts  of 
the  country  during  the  summer,  and  below  it  during  the 
winter.  They  are  observed  mostly  in  equatorial  and  tropical 
latitudes,  because  here  the  diurnal  range  of  temperature  is 
greatest,  and  consequently  there  are  the  greatest  contrasts  be- 
tween land  and  ocean  temperatures ;  but  they  are  also  quite 
common  in  middle  latitudes,  and  likewise  traces  of  them  were 
found  by  Scoresby  in  Greenland  during  calm  and  clear  weather*. 
These  winds,  for  reasons  already  given  (§  132),  are  light  winds. 


22O  MONSOONS,  AND   LAND-  AND   SEA-BREEZES. 

except  where  there  are  high  lands  or  mountain  ranges  near  the 
coast,  and  extend  no  great  distance  from  the  shore  either  inland 
or  out  into  the  sea.  They  depend  upon  the  thermal  conditions 
mostly  in  the  vicinity  near  the  coast,  and  but  little  upon  those 
at  a  great  distance  toward  the  interior  of  continents.  They 
are,  therefore,  where  there  are  no  other  causes  of  disturbance, 
in  a  direction  perpendicular  to  the  general  trend  of  the  coast 
— inward  toward  the  land  during  the  day,  and  the  reverse  at 
night. 

As  weak  monsoon  influences,  such  as  those  of  Australia,  are 
-often  not  sufficient  to  reverse  the  general  currents  of  the  at- 
mosphere, such  as  the  trade-winds  and  the  general  westerly 
*and  southwesterly  winds  of  the  middle  latitudes,  but  merely  to 
cause  annual  oscillations  in  their  strength  and  direction,  so  land- 
and  sea-breezes  are  entirely  overwhelmed  and  not  observable 
where  there  are  other  strong  prevailing  currents,  either  of  the 
general  circulation  of  the  atmosphere,  or  of  monsoons,  or  other 
more  local  and  temporary  disturbances  to  be  treated  farther 
on,  or,  if  observable  at  all,  it  is  merely  their  effect  in  causing 
diurnal  variations  of  strength  and  direction.  For  instance,  if 
there  is  a  prevailing  wind  of  considerable  strength  from  the 
ocean  inland,  the  effect  of  the  sea-breeze  influence  would  be 
superadded  to  this  during  the  day  and  increase  its  strength, 
while  at  night  the  contrary  influence  would  not  be  sufficient  to 
entirely  counteract  and  reverse  [it  and  cause  a  wind  from  the 
land  toward  the  sea,  but  might  diminish  very  much  its  strength. 
Likewise,  if  the  prevailing  wind  were  in  the  direction  of  the 
general  trend  of  the  coast,  the  effect  of  the  land-  and  sea-breeze 
influence  would  be  to  cause  the  wind  to  incline  in  toward  the 
land  during  the  day  and  away  from  it  during  the  night,  more 
or  less  according  to  the  comparative  strength  of  the  disturbing 
influence.  The  pure  land-  and  sea-breezes  are  observed  in 
•calm  weather  only,  and  of  course  mostly  in  clear  weather, 
when  the  changes  of  temperature  between  day  and  night  are 
the  greatest.  Along  the  coasts  of  India,  therefore,  and  in  all 
monsoon  regions,  they  are  only  observed  for  a  few  weeks  at 
the  times  of  the  reversals  of  the  monsoon  in  spring  and  fall, 


LAND-   AND   SEA-BREEZES.  22 I 

when  calms  prevail,  unless  there  are  prevailing  winds  from  other 
causes  than  those  of  the  monsoons. 

152.  As  the  effect  of  the  monsoon  influence  first  begins  to 
be  seen  in  the  spring  as  the  temperature  of  the  continent  first 
rises  above  that  of  the  oceans,  is  the  greatest  in  midsummer, 
and  is  reversed  in  the  fall  into  the  winter  monsoon  as  the  tem- 
perature of  the  land  falls  below  that  of  the  ocean,  and  this  has 
its  greatest  strength  in  midwinter,  so  the  pure  sea-breeze  is 
first  felt  in  the  forenoon  about  10  o'clock,  when  the  tempera- 
ture of  the  adjacent  land  becomes  greater  than  that  of  the  sea,. 
is  greatest  at  about  3  o'clock  in  the  afternoon,  during  the 
warmest  part  of  the  day,  and  is  then  reversed  into  a  land- 
breeze  about  8  o'clock  in  the  evening,  when  the  temperature  of 
the  land  becomes  greater  than  that  of  the  ocean ;  and  this  has 
its  greatest  strength  early  in  the  morning,  when  the  tempera- 
ture is  the  lowest. 

The  effect  of  the  land-wind  upon  the  calm  smooth  ocean  in 
the  forenoon  is  usually  observed  first  near  shore,  and  as  the 
strength  of  the  breeze  increases  it  extends  gradually  back  from 
the  land  into  the  ocean.  But  the  reverse  of  this,  according  to 
Dampier,  is  often  observed.  It  no  doubt  depends  upon  local 
circumstances.  In  the  case  of  the  true  sea-breeze,  depending 
simply  upon  contrast  of  temperature  between  the  level  coast  and 
the  ocean,  the  greatest  thermal,  and  consequently  the  greatest 
pressure,  gradient  is  first  caused  at  and  near  the  coast,  where 
there  is  an  abrupt  change  of  temperature  between  land  and 
sea ;  and  therefore  the  interchange  of  air  between  sea  and  land 
must  first  commence  there,  and  gradually  extend  to  greater  dis- 
tances, both  inland  and  out  into  the  sea,  as  the  temperature 
differences  increase  toward  the  middle  of  the  day.  In  the  case, 
however,  of  the  strong  sea-winds  experienced  along  coasts 
where  there  are  steep  slopes  from  high  lands  and  mountain 
ranges  near,  it  is  reasonable  to  suppose  that  the  interchange 
may  commence  first  between  these  slopes  and  the  sea  at  a  dis- 
tance, and  be  gradually  communicated  to  the  air  on  the  coast, 
and  so  the  effect  would  first  be  seen  at  a  distance,  and  only 
afterwards  near  the  coast. 


'222  MONSOONS,  AND   LAND-  AND   SEA-BREEZES. 

For  the  same  reason  that  the  summer  monsoons  are  stronger 
than  the  winter  ones  in  equatorial  and  tropical  latitudes  (§  145), 
are  the  sea-breezes  here  stronger  than  the  land-breezes.  Many 
evidences  of  this  fact  might  be  cited  here,  and  this  has  been 
especially  observed  frequently  along  the  coast  of  the  Gulf  of 
Guinea  by  many  others,  as  well  as  somewhat  recently  by  Com- 
mander Burke,  R.  N.  He  says:37 

"  The  winds  that  prevail  along  these  coasts  are  already  so  well  known 
as  to  render  much  comment  unnecessary,  the  usual  sea-  and  land-breezes 
being,  with  few  exceptions,  constant;  the  latter,  however,  are  nowhere 
very  strong,  and  as  a  rule  are  not  felt  before  midnight,  nor  do  they  last 
later  than  8  A.M.  The  sea-breeze  commences  at  about  10  A.M.,  reaches 
its  maximum  strength  at  4  P.M.,  and  then  gradually  falls  light;  but  fre- 
quently, and  especially  in  the  Gulf  of  Guinea,  it  maintains  its  full 
strength  until  it  suddenly  drops  and  gives  place  to  the  land-breeze." 

The  strong  land-  and  sea-winds  along  coasts  with  long  slopes 
from  highlands  and  mountain  ranges  depend  very  much  upon 
the  configuration  of  such  coasts.  Around  high  promontories 
they  are  comparatively  weak,  because  the  area  heated  above 
•or  cooled  below  the  temperature  of  the  sea  is  small,  and  the 
effect  is  distributed  around  over  a  comparatively  large  area. 
On  the  contrary  in  a  narrow  bay  surrounded  by  high  hills  or 
mountains  the  effect  of  the  heated  or  cooled  slopes  all  around 
is  concentrated  upon  a  comparatively  small  space.  The  cooled 
stratum  of  air  at  night  in  contact  with  the  hill-sides  flows  in 
irom  all  sides  toward  the  bay  with  a  concentrated  effect  at  the 
lower  part  of  the  bay,  or  at  the  common  outlet  of  several  val- 
leys which  come  together,  just  as  floods  from  the  concentrated 
water  of  heavy  rains  increase  in  volume  and  force  as  the 
streams  from  all  sides  come  into  one  large  river  in  the  valley. 
Hence  it  is  said,18  "  The  land-breeze  frequently  comes  off  in 
sharp,  sometimes  in  dangerous,  squalls  ;  and  our  Sailing  Direc- 
tions are  full  of  cautions  to  navigators  to  look  out  for  the  first 
•squalls  of  the  land-breeze :  even  when  it  does  not  come  in 
squalls,  it  comes  quickly." 

On  the  contrary,  the  sea-winds  are  strengthened  in  the 
same  proportion,  for  when  the  surfaces  of  the  hill-sides  are  as 


MOUNTAIN  AND    VALLEY    WINDS.  22$ 

•much  heated  above  the  temperature  of  the  ocean  and  the 
superincumbent  air  at  the  same  levels  above  it,  the  air  tends  to 
rush  up  the  slopes  and  hill-side  valleys  with  the  same  force  as 
it  flows  down  when  they  are  as  much  cooled  below  this  tem- 
perature, and  the  air  which  is  drawn  up  at  all  sides  over  a  com- 
paratively large  area  is  drawn  up  the  bay  and  gives  rise  to 
.a  strong  wind. 

MOUNTAIN  AND   VALLEY  WINDS. 

153.  On  the  slopes  of  mountain  ranges  and  the  plains  near 
the  base,  and  especially  in  deep  valleys  extending  from  the 
slopes  into  the  country  below,  there  are  often  strong  winds, 
toward  and  up  the  mountain  side  during  the  day,  and  the 
reverse  at  night.  This  fact  is  well  known  to  hunters  and  all 
who  are  accustomed  to  encamp  in  the  mountains  at  night;  and 
;so  the  camp-fires  are  always  placed  below  the  tents  on  the 
slope,  that  the  smoke  may  be  drawn  away  by  the  descending 
current,  instead  of  being  blown  toward  them.  Such  currents 
of  course  extend  to  some  distance  over  the  plain  below,  and 
^vhere  the  air  is  brought  together  by  a  number  of  ravines  and 
deep  valleys  into  one  common  and  somewhat  contracted  cur- 
rent below,  the  force  of  the  wind  may  be  very  great.  Just  the 
reverse  takes  place  during  the  day,  for  the  air  then  rushes  up 
the  mountain  side  from  the  plain  below,  and  if  this  air  is  con- 
centrated into  narrow  valleys,  either  near  the  base  of  the 
mountain  or  up  the  side,  the  current  becomes  unusually 
strong. 

R.  Strachey,  Esq.,  of  the  Bengal  Engineers,  in  the  2ist  Vol. 
Royal  Geog.  Soc.,  as  given  by  Espy,  says  : 

"  The  winds  in  the  mountains  of  the  Himalayas  blow  up  the  valley 
during  the  day  from  9  A.M.  to  9  P,M.,  and  down  during  the  correspond- 
ing hours  of  the  night.  At  the  debouches  of  the  principal  streams  into 
the  plains  these  night-winds  blow  with  great  violence,  particularly  in 
the  winter.  They  diminish  in  force  as  we  ascend  the  mountains,  and  at 
great  elevations  and  in  the  plains  of  western  Thibet  the  nights  are 
almost  perfectly  calm.  The  diurnal  winds,  on  the  other  hand,  in  the 
latter  country  are  terrific;  and  in  travelling  there  we  looked  forward  to 
the  afternoon,  when  the  winds  were  at  their  height,  with  real  dread." 


224  MONSOONS,  AND  LAND-  AND   SEA-BREEZES. 

At  the  time  of  the  total  solar  eclipse  on  the  2Qth  of  July,, 
1878,  the  writer  ascended  about  midday  the  eastern  slope  of 
the  mountain  to  the  top  of  Gray's  Peak  in  Colorado,  where  the 
eclipse  was  total.  The  day  was  almost  perfectly  clear,  and  the 
wind  above,  as  indicated  by  the  motion  of  a  few  specks  of 
cloud,  was  westerly.  On  the  way  up  the  mountain  there  was 
a  very  strong  current  rushing  directly  up  the  mountain,  such 
that  it  was  necessary  to  hold  on  to  one's  hat  with  one  hand  to 
keep  it  from  being  blown  away.  This  was  met  by  the  westerly 
wind  above  and  by  a  similar  current  up  the  west  side,  but  of 
less  strength  because  the  slope  was  not  so  long.  On  the  crest 
of  the  mountain,  a  few  rods  in  width,  there  was  a  calm,  for  the 
ascending  currents  from  each  side  after  meeting  continued  on 
upward,  which  was  indicated  by  some  of  the  writer's  note- 
paper,  on  stepping  down  the  east  side  a  few  rods,  being  caught 
and  carried  vertically  up  to  a  considerable  height,  and  after- 
wards falling  back  again  near  the  same  spot. 

On  the  descent,  late  in  the  afternoon,  there  was  a  perfect 
calm,  the  mountain  slope  being  now  cooled  down  to  about 
the  mean  temperature  of  the  day.  During  the  night,  especi- 
ally in  the  latter  part  of  it,  there  was,  no  doubt,  a  reverse 
current  down  the  mountain  of  about  the  same  strength,  and 
continuing  until  about  the  middle  of  the  forenoon. 

These  winds  depend  upon  the  same  circumstances  and  are 
explained  upon  precisely  the  same  principles  as  the  land-  and 
sea-breezes  on  mountain  slopes  along  sea-coasts ;  in  fact,  the 
only  difference  is  in  the  circumstance  that  in  the  one  case  there 
is  ocean  and  in  the  other  a  plain  at  the  base  of  the  slope. 

154.  A  similar  but  much  feebler  effect  is  observed  on  long 
declivities  of  open  country  with  only  a  very  small  gradient, 
such  as  that  between  the  Mississippi  valley  and  the  Rocky 
Mountains  ;  but  in  such  cases  it  is  generally  somewhat  masked 
by  other  prevailing  currents,  so  that  there  is  not  a  complete 
reversion  of  the  wind,  but  a  diurnal  change  of  its  direction.. 
The  writer  has  often  observed  in  Missouri  and  Kansas  during 
clear  warm  weather,  when  the  prevailing  wind  is  generally 
southerly  or  a  little  west  of  south,  that  in  the  morning  when> 


MOUNTAIN  AND    VALLEY    WINDS.  22$ 

the  surface  air  is  cooled  down  and  tends  to  flow  down  the  in- 
cline, the  wind  is  southwesterly,  but  as  the  heat  of  the  day 
increases  it  gradually  changes  around  toward  the  south,  and 
toward  evening  is  from  a  southeasterly  direction,  the  tendency 
now  being  for  the  heated  surface  air  to  move  gently  up  the 
slope  toward  the  mountains.  But  during  the  night,  if  no  ab- 
normal disturbance  of  any  kind  takes  place,  it  always  gets  back 
again  to  a  southwesterly  direction. 


CHAPTER  VI. 
CYCLONES. 

155.  IN  preceding  chapters  we  have  considered  the  general 
circulation  of  the  atmosphere  which  would  arise,  upon  an 
earth  with  a  homogeneous  and  smooth  surface,  from  a  regular 
temperature  gradient  between  the  equator  and  the  poles,  with- 
out regard  to  differences  of  temperature  in  different  longitudes 
on  the  same  parallels  of  latitude.  Such  a  gradient  is  deducible 
from  the  normals  of  latitude  given  in  the  table  of  §  68.  This 
gradient,  it  is  seen,  varies  with  the  seasons  of  the  year,  being 
greatest  in  winter  and  least  in  summer,  and  hence  there  is  an 
annual  variation  in  the  general  motions  of  the  atmosphere, 
which  has  likewise  been  considered.  But  upon  the  earth's  sur- 
face as  it  actually  exists  there  are  mountain  ranges  and  irregu- 
lar distributions  of  land  and  water,  and  the  effects  of  these  in 
disturbing  the  regularity  of  the  general  motions  by  means  of 
deflections  and  the  differences  in  the  frictional  resistances  on 
different  parts  of  the  earth's  surface,  and  especially  between 
the  two  hemispheres,  have  been  pointed  out. 

The  temperature  gradient  from  which  this  general  but  dis- 
turbed circulation  of  the  atmosphere  at  any  time  arises,  de- 
pends upon  the  difference  between  the  mean  diurnal  vertical 
intensity  of  solar  radiation  upon  the  earth's  surface  between 
the  equatorial  and  polar  regions,  which,  though  variable,  never 
vanishes,  and  hence  the  general  motions  of  the  atmosphere  are 
variable,  but  never  cease.  The  general  circulation  also  consists 
of  two  systems,  which  are  similar,  except  so  far  as  they  are 
disturbed  on  account  of  a  non-homogeneity  of  the  earth's 
surface,  each  of  which  extends  over  a  whole  hemisphere. 

226 


VERTICAL   CIRCULATION.  22? 

Subsequently  .another  class  of  temperature  disturbances 
ivere  considered — those  arising  from  the  abnormals  of  latitude 
at  any  time,  giving  rise  to  monsoons  and  land-  and  sea-breezes. 
These  are  fixed  in  locality,  and  extend  mostly  over  large  areas 
of  the  earth's  surface,  but  are  subject  to  annual  and  diurnal 
changes,  and  even  to  complete  reversals  with  a  cessation  of 
motion  at  the  time  of  reversal,  so  far  as  it  depends  on  the  mon- 
rsoon  influence,  and  sensibly  so  for  some  little  time  immediately 
before  and  after. 

We  come  now  to  the  consideration  of  another  class  of  tem- 
perature disturbances,  which  extend  over  a  comparatively  small 
part  of  the  earth's  surface  and  are  mostly  neither  fixed  to  any 
given  part  of  the  earth's  surface,  nor  do  they  continue  gener- 
.ally  for  a  great  length  of  time,  and  hence  they  are  of  a  more 
local  and  temporary  character  than  the  others.  In  these  there 
is  a  gyratory  motion  of  the  air  around  some  central  point,  and 
.hence  they  are  called  cyclones. 

VERTICAL  CIRCULATION. 

156.  If  the  air  over  any  portion  of  the  earth's  surface  is 
warmer  at  all  altitudes  than  that  of  the  surrounding  parts  at 
the  same  levels,  it  is  lighter,  and  tends  to  rise  up  above  its 
original  level,  and  flow  out  in  all  directions  above.  This  de- 
creases the  pressure  at  the  earth's  surface  over  this  area,  but 
increases  it  a  little  over  the  surrounding  parts  ;  and  thus  there 
arises  a  gradient  of  pressure  decreasing  from  the  exterior  to- 
ward the  interior  below,  which  causes  a  flow  of  air  in  from  all 
sides  to  supply  the  ascending  current.  There  is  thus  a  verti- 
cal circulation  and  interchange  of  air  between  the  interior  and 
exterior  parts  established,  just  as  in  the  case  of  the  general  cir- 
culation of  the  atmosphere  (§  72),  except  that  now  the  motion 
is  toward  the  central  part  below  and  from  it  above,  while  in  the 
general  circulation  it  is  toward  the  polar  central  region  above 
^and  from  it  below,  the  central  region  in  this  case  being  colder 
instead  of  warmer  than  the  surrounding  parts. 

It  is  not  necessary,  however,  in  order  to  have  such  a  circu- 


228  CYCLONES. 

lation,  that  all  the  strata  of  air  from  bottom  to  top  shall  be: 
warmer  in  the  interior  than  in  the  surrounding  parts,  but  only 
that  there  shall  be  such  a  disturbance  of  the  equality  of  tem- 
perature that  the  pressure  of  any  part  of  the  interior  is  less 
than  that  of  the  exterior  part ;  for  where  this  is  the  case  the  air 
tends  to  rise  up,  and  that  of  greater  pressure  at  the  same  level 
to  flow  in  and  takes  its  place,  and  thus  the  circulation  is  estab- 
lished. In  general  the  velocity  of  the  ascending  current  in  the 
interior  part  is  much  greater,  but  over  a  smaller  area,  than 
that  of  the  descending  current  in  the  exterior  surrounding  part 
over  a  much  greater  area,  where  it  is  simply  a  very  gradual 
settling  down  ;  for  since  there  is  no  definite  limit,  the  tendency 
is  for  the  air  above  to  flow  out  to  still  greater  distances,  and  thus- 
to  press  down  and  bring  in  the  air  below  from  greater  distances. 

On  account  of  the  non-homogeneity  of  the  earth's  surface, 
comprising  hills  and  valleys,  land  and  water,  and  dry  and 
marshy  areas,  all  with  different  radiating  and  absorbing  powers, 
and  also  on  account  of  the  frequent  irregular  and  varying  dis- 
tribution of  clouds,  it  must  often  happen  that  there  are  consid- 
erable local  departures  of  temperature  from  that  of  the  sur- 
rounding parts  ;  and  if  it  should  so  happen,  as  it  frequently 
must,  that  this  area  is  of  a  somewhat  circular  form,  and  the  air 
has  a  temperature  higher  than  that  of  the  surrounding  part  of 
the  atmosphere,  then  we  have  the  conditions  required  to  give 
rise  to  a  vertical  circulation,  with  an  ascending  current  in  the 
interior,  as  described  above.  But  unless  there  is  some  source 
of  heat  by  which  this  interior  higher  temperature  is  kept  up, 
this  circulation  soon  ceases,  for  the  interchange  of  air  between 
the  interior  and  exterior  parts  of  the  air  comprised  in  the  cir- 
culation tends  to  continually  reduce  the  difference  of  tempera- 
ture upon  which  the  circulation  depends,  and  to  bring  all  parts 
to  the  same  temperature. 

157.  It  has  been  shown  (§  29)  that  if  any  portion  of  the 
atmosphere,  when  it  is  in  the  unstable  state,  receives,  from  any 
slight  temperature  or  other  disturbance,  an  upward  motion,  it- 
becomes  warmer  than  the  surrounding  air  at  the  same  level ;  and 
the  tendency  then  is  for  it  to  continue  to  rise  as  long  as  the. 


VERTICAL    CIRCULATION.  22$ 

air  is  in  the  unstable  state,  and  thus  to  give  rise  to  a  vertical 
circulation,  and  this  must  continue  as  long  as  the  atmosphere 
of  the  surrounding  parts  is  in  the  unstable  state.  Let  us  con- 
sider first  the  case  of  a  dry  atmosphere,  and  suppose,  as  in  the 
example  previously  given  (§  29),  that  the  vertical  temperature 
gradient  is  that  of  a  decrease  of  i.°2  for  each  100  meters  of  in- 
crease of  altitude.  In  this  case  the  air  of  the  ascending  current 
becomes  warmer  than  that  of  the  comparatively  slow  descend- 
ing; current  on  all  sides  at  the  same  level  at  the  rate  of  o°.2 

o 

for  each  100  meters  of  ascent  ;  and  so  the  temperature  dif- 
ferences and  the  force  by  which  the  vertical  circulation  is 
kept  up  increase  at  first  until  this  circulation  is  fully  estab- 
lished and  air  has  ascended  from  the  earth's  surface  up  to 
the  upper  strata,  after  which  it  gradually  decreases  ;  for  the  in- 
terchange of  air  between  the  lower  and  upper  strata  tends  to 
reduce  the  temperature  gradient  of  all  of  it  to  that  of  the  in- 
different state,  which  is  i°  for  each  100  meters  of  difference  of 
altitude,  and  the  horizontal  interchange  tends  to  equalize  the 
temperatures  between  the  interior  and  exterior  parts  of  the  cir- 
culation, and  when  this  equality  takes  place  all  force  to  keep 
up  the  circulation  vanishes.  Of  course  the  more  the  unstable 
:state  differs  from  the  indifferent  state,  the  greater  the  energy 
which  maintains  the  circulation,  and  the  greater  the  rapidity 
of  this  circulation.  But  in  all  cases  there  is  probably  such 
an  interchange  and  inversion  of  the  air  of  the  lower  and  upper 
strata  that  the  unstable  state  is  soon  broken  up  and  the  circu- 
lation ceases. 

In  the  case  supposed  above,  of  a  regular  and  uniform  verti- 
cal temperature  gradient  at  all  altitudes,  the  differences  of  tem- 
perature at  the  same  levels  between  the  ascending  air  and  that 
of  the  surrounding  air  would  increase  with  increase  of  altitude ; 
but  such  gradients  are  by  no  means  uniform,  but  may  so 
change  at  different  altitudes  that  the  atmosphere  may  be  in  the 
unstable  state  below  and  the  stable  state  above,  or  vice  versa. 
In  the  first  case  the  ascending  air  would  first  become  warmer, 
the  differences  then  decrease,  and  finally  the  ascending  air  be- 
come colder  than  that  of  the  surrounding  air  at  the  same  lev- 


230  CYCLONES. 

els,  but,  still  the  vertical  circulation  would  take  place,  thougb 
its  energy  would  be  less,  and  it  would  not  generally  extend  up 
to  the  top  of  the  atmosphere. 

158.  In  the  case  of  a  moist  atmosphere  with  the  unstable 
state  for  dry  air,  we  have  the  same  energy  for  originating  and 
maintaining  a  vertical  calculation  as  in  the  case  of  dry  air,  with 
the  additional  energy  of  all  the  latent  heat  of  the  aqueous 
vapor  set  free  in  its  condensation  in  the  ascending  current,  and 
this  latter  is  a  continuous  source  of  energy  as  long  as  moist  air 
is  being  drawn  in  from  all  sides  to  supply  this  current.  For  in- 
stance, suppose  the  air  is  saturated,  and  is  in  the  unstable  state 
for  dry  air,  then  at  the  first  upward  start  of  the  air  it  be- 
comes warmer  than  the  surrounding  air  and  the  tendency  is  to 
continue  on.  As  soon  as  the  vertical  circulation  is  fully  estab^ 
lished,  the  vertical  gradient  in  this  ascending  current  becomes 
that  given  by  Table  III,  which  is  greater  or  less  according  to> 
the  season  of  the  year  and  the  altitude.  With  a  summer  tem- 
perature of  30°  at  the  earth's  surface,  as  may  be  seen  from  the 
example  given  in  §  27,  the  rate  of  decrease  of  temperature  is 
only  about  o°.37  for  each  100  meters  of  ascent  up  to  an  alti- 
tude of  4000  meters,  and  even  up  to  much  greater  altitudes 
the  rate  would  vary  but  little  from  this.  If  the  vertical  gradi- 
ent of  unstable  equilibrium  were  i°.2,  as  assumed  in  the  pre- 
ceding case,  we  should  have,  after  vertical  circulation  was  first 
fully  established,  a  difference  of  temperature  between  the  air 
of  the  ascending  current  and  that  of  the  comparatively  quiet 
surrounding  air  of  nearly  o°.83  for  each  100  meters  of  altitude  ; 
for  at  this  time  the  vertical  temperature  gradient  of  the  very 
slowly  descending  air  over  a  very  large  area  will  not  have 
changed  much.  In  the  case  of  dry  air  it  was  only  o°.2  for  the 
same  vertical  temperature  gradient;  and  so  of  the  o°.83  above, 
o°.63  is  due  to  the  heat  of  condensation  of  the  vapor. 

If  the  atmosphere  were  not  completely  saturated,  but  had 
a  depression  of  the  dew-point — air-temperature  minus  temper- 
ature of  the  dew-point — of  8°,  then  by  Table  IV  the  air  at  the 
earth's  surface  would  have  to  ascend  about  1000  meters  before: 
condensation  would  commence,  and  in  this  part  of  the  ascent 


VERTICAL    CIRCULATION.  23 1 

the  rate  of  the  cooling  would  be  i°  instead  of  o°.37  for  each 
100  meters,  after  which  the  latter  rate  would  take  place. 
Hence  in  this  case  the  whole  of  the  ascending  column  would 
have  a  lower  temperature  than  in  the  preceding  case  of  com- 
plete saturation,  being,  above  the  altitude  of  1000  meters,  equal 
to  10  X  (i°.o  —  o°.37)  —  6°. 3  less  than  in  the  case  of  complete 
saturation,  and  hence  the  energy  of  the  vertical  circulation 
would  be  much  less  in  consequence  of  the  lack  of  complete 
saturation. 

In  the  preceding  examples  we  have  assumed  a  uniform  ver- 
tical gradient  which  makes  a  dry  atmosphere  unstable.  But 
this  is  not  necessary  in  the  case  of  a  moist  atmosphere,  in  order 
to  produce  a  vertical  circulation.  In  fact,  in  the  case  of  com- 
plete saturation  it  is  only  necessary  that  this  gradient  shall  be 
a  little  greater  than  that  given  by  Table  III,  which  in  the  last  ex- 
ample is  o°.37  for  each  100  meters.  If  the  gradient  were  o°.8,  a 
little  less  than  that  of  the  indifferent  state  for  dry  air,  then 
each  part  of  the  air  at  all  altitudes,  in  its  initial  ascent  of  100 
meters,  would  be  o°.8  —  o°.37  =  o°.43  warmer  than  the  sur- 
rounding undisturbed  air  at  the  same  levels ;  and  after  vertical 
circulation  were  fully  established,  and  air  had  ascended  from 
the  earth's  surface  up  to  high  altitudes,  the  differences  of  tem- 
perature would  be  o°.43  for  each  100  meters  up  to  these  alti- 
tudes, and  so  in  the  upper  strata  of  the  air  they  would  be  very 
great.  If  the  vertical  gradient  were  still  less  but  a  little 
greater  than  o°.37,  these  differences  would  be  smaller,  and  the 
force  would  be  able  to  give  rise  to  and  maintain  a  compara- 
tively feeble  circulation  only. 

159.  In  the  case  in  which  the  atmosphere  is  not  completely 
saturated,  we  have  seen  that  in  the  first  ascent  of  the  air,  until 
it  is  cooled,  at  the  rate  of  i°  for  each  100  meters,  down  to  the 
dew-point,  it  becomes  colder  and  heavier  than  the  surrounding 
air,  unless  the  atmosphere  is  in  the  unstable  state  for  dry  air. 
It  may,  therefore,  happen  that  before  the  air  rises  up  to  the 
altitude  where  condensation  takes  place  the  whole  air-column 
may  be  heavier  than  a  similar  one  of  the  surrounding  part  of 
the  atmosphere.  In  this  case  there  must  be  more  than  a  mere 


232 


CYCLONES. 


initial  and  temporary  impulse,  or  very  slight  temperature  dis- 
turbance merely,  to  start  the  vertical  ascent  of  the  air.  The 
initial  temperature  of  the  air  before  ascent  commences  must 
be  so  much  greater  than  that  of  the  surrounding  air,  that  it 
does  not  become  cooled  down  in  its  first  ascent,  before  conden- 
sation takes  place,  to  a  lower  temperature,  on  the  average  for 
the  whole  column,  than  that  of  the  surrounding  air. 

This  will  be  better  understood  by  tracing  the  effects  which 
must  follow  in  a  few  assumed  cases.  In  the  following  table 
the  first  column  contains  the  altitudes  of  several  successive 
strata  at  equal  intervals,  and  the  column  A  the  corresponding 
temperatures  of  the  air  in  its  undisturbed  state  as  it  existed 
very  nearly  on  the  average  of  Glaisher's  balloon  ascensions  in 
clear  weather,  as  given  in  the  table  of  §  27,  assuming  that  the 
temperature  at  the  earth's  surface  was  25°  C.: 


SATURATED 

o 

—  ,/  QO 

Q 

Altitudes 
in 

AIR. 

—  4 

=  4° 

Meters. 

A 

B 

C 

B' 

C' 

D 

E 

F 

G 

H 

I 

K 

6000 

-3°.o 

-4°.  3 

~2°-5 

-60.5 

-3°  -5 

-14°  o 

—  2O°.  0 

-  9°-  3 

-39°-  5 

-43°-o 

-47°-  5 

-60° 

5500 

x  -5 

—  2  .7 

+°  -3 

-5  -o 

—  o  .7 

12   0 

18  .0 

6  .y 

38  -5 

4t  -5 

42  .9 

55 

5000 

0  .0 

—  o  .8 

3  -o 

—  3  -3 

2  .0 

10  4 

15  .5 

4  -5 

37  -o 

39  -5 

38  -5 

50 

4500 

—  |—  i  .  7 

+i  -3 

5  -5 

—  i  .4 

4  -5 

8  o 

13  .0 

-  i  .9 

35  -o 

36  .8 

34  -o 

45 

4000 

3  -6 

3  -3 

7  -8 

o  .6 

4  -8 

5  5 

10  .0 

+  o  .7 

32  -5 

33  -8 

29  -7 

40 

3500 

5  .6 

5  -5 

IO  .  I 

+2  .8 

8  .1 

-  3 

7  -° 

3  -2 

29  -5 

25  -4 

35 

3000 

7  -8 

8  .1 

12  .4 

5  -3 

10  .4 

0 

-3-5 

5  -7 

26  .0 

26  !o 

21  .3 

30 

2500 

10  .3 

10  .7 

14  .6 

7  -8 

12  .6 

+  3 

o  .0 

8  .1 

22  .0 

21  .7 

T7  -3 

25 

2000 

12  .8 

13  -3 

16  .7 

10  .4 

14  .7 

6  . 

+  4  -0 

10  .4 

18  .0 

17  .4 

13  .6 

20 

1500 

15  '4 

15  -9 

18  .8 

13  .0 

16  .8 

10  . 

9  .0 

12  .7 

13  -8 

13  -o 

10  .0 

15 

IOOO 

18  .8 

19  .0 

20  .9 

16  .0 

18  .9 

14  • 

15  .0 

15  .0 

9  -5 

8  .4 

6  .6 

10 

500 

21  .0 

23  -o 

23  .0 

20  .0 

20  .0 

19  .0 

20  .0 

20  .0 

-5  -o 

-5  -o 

~3  -2 

—  5 

000 

25  -o 

25  .0 

25  .0 

25  .0 

25  .0 

25  .0 

+25  .0 

+25  -o 

o  .0 

o  .0]   o  .0 

0 

The  columns  B  and  C  in  the  case  of  saturated  air  represent 
— the  first  the  temperatures  which  the  air  of  each  stratum  would 
have  after  ascending  through  500  meters  to  the  stratum  above 
as  given  in  the  preceding  table  ;  and  the  second,  the  tempera- 
tures at  the  different  altitudes  after  the  vertical  circulation  has 
been  fully  established  and  the  air  has  ascended  from  the  earth's 
surface  high  up  into  the  upper  strata,  both  being  determined 
by  the  rates  of  cooling  of  ascending  air  given  in  Table  III. 
By  comparing  B  and  A  it  is  seen  that,  after  this  initial  start, 
the  temperature  of  the  ascending  air  is  warmer  than  that  of 
the  surrounding  and  sensibly  undisturbed  air  up  to  the  altitude 


VERTICAL    CIRCULATION.  233 

<of  3500  meters,  so  that  up  to  that  altitude  the  atmosphere  is  in 
the  unstable  state,  and  the  air  being  once  started  upward  by 
any  slight  impulse  or  temperature  disturbance,  the  tendency  is 
to  go  on  ;  but  above  the  altitude  of  3500  meters  with  any 
small  initial  ascent,  it  becomes  colder  and  heavier  than  the  sur- 
rounding undisturbed  air,  and  so  is  deflected  off  horizontally  in 
.all  directions  from  the  central  part  of  the  ascending  air  outward, 
and  a  vertical  circulation  commences.  As  this  progresses  the 
vertical  gradient  gradually  approximates  to  that  of  a  fully-estab- 
lished current,  and  the  temperatures  become  those  of  the  col- 
umn C.  By  comparing  these  temperatures  with  those  of  A,  it 
is  seen  that  the  temperatures  of  the  ascending  air  are  greater 
than  those  of  the  undisturbed  air  at  the  same  altitudes,  even 
far  above  the  altitude  of  6000  meters,  and  the  tendency  for  it 
to  continue  to  ascend  is  then  very  strong.  With  the  vertical 
decrease  of  temperatures,  therefore,  of  the  column  A,  in  the 
•case  of  completely  saturated  air,  it  would  be  possible  for  a  cy- 
clonic disturbance  of  the  atmosphere  to  originate  from  a  very 
small  initial  disturbance,  and  after  being  fully  established,  to 
have  considerable  violence.  But  as  the  air  above  in  this  case 
in  its  initial  ascent  becomes  colder  and  heavier  than  the  sur- 
rounding air,  the  vertical  circulation  may  not  extend  very  high 
.before  it  is  deflected  off  laterally;  but  it  must  extend  higher 
than  the  limit  of  the  unstable  state  on  account  of  the  momen- 
tum which  it  acquires  below  in  its  ascent. 

If  instead  of  a  very  small  temperature  or  other  disturbance 
by  which  initial  ascending  currents  are  induced  over  a  given 
area,  we  suppose  the  temperature  of  the  interior  part  of  the  air 
over  this  area  to  be  several  degrees  higher  than  that  of  the 
surrounding  undisturbed  parts,  then  this  number  of  degrees 
must  be  added  to  columns  B  and  C ;  and  then,  it  is  seen,  both 
the  initial  force  and  that  after  the  vertical  circulation  is  fully 
established  are  very  much  increased  as  long  as  this  difference 
of  temperature  between  the  central  and  surrounding  parts  re- 
mains, and  a  vertical  circulation  might  originate  in  this  case  if 
the  vertical  temperature  gradient  were  even  considerably  less 
than  that  of  column  A.  But  as  the  vertical  circulation  contin- 


234  CYCLONES. 

ues,  this  difference  of  temperature  is  gradually  diminished  by 
the  interchange  of  air  between  the  central  and  exterior  parts, 
and  likewise  the  general  vertical  temperature  gradient  of  the 
whole  atmosphere  for  a  long  distance  all  around  is  gradually 
brought  to  that  of  the  indifferent  state  for  saturated  air,  just 
as  in  the  case  of  dry  air  (§  157),  and  then  the  whole  force  van- 
ishes. 

160.  With  the  same  vertical  temperature  gradient  of  the 
atmosphere  generally  over  a  large  extent  of  the  earth's  surface, 
represented  by  column  A,  let  us  consider  the  case  in  which 
the  air  is  not  completely  saturated,  but  in  which  there  is  a 
given  difference  between  the  temperature  of  the  air,  r,  and  that 
of  the  dew-point,  d,  or  a  depression  of  the  dew-point,  T  —  d,  at 
all  altitudes.  In  this  case  the  air  in  its  initial  disturbance  has 
to  rise  at  all  altitudes,  by  Table  IV,  about  125  meters  for  each 
degree  Centigrade  of  r  —  d  before  condensation  and  cloud  for- 
mation take  place,  and  during  this  time  the  rate  of  cooling  is 
i°  for  each  100  meters,  the  same  as  in  dry  air.  If  we  take  r  —  d 
•=  4°,  then  the  air  of  each  stratum  in  ascending  through  500 
meters  is  cooled  down  to  the  dew-point  and  condensation 
commences,  after  which  the  rate  of  cooling  is  that  given  by 
Table  III,  and  consequently  differs  at  different  altitudes  and, 
temperatures.  After  the  air  of  each  stratum  from  any  supposed 
initial  impulse  has  ascended  to  the  one  500  meters  above,  the 
temperatures  become  those  of  the  column  B',  instead  of  those 
of  A,  which  represent  the  temperatures  of  the  surrounding  air 
which  has  riot  ascended.  By  comparing  B'  with  A  it  is  seen 
that  the  ascending  air  has  now  become  colder,  and  conse- 
quently heavier  than  the  surrounding  undisturbed  air,  and  has 
no  tendency  to  ascend  higher,  unless  the  ascent  is  maintained 
by  the  initial  starting  force,  but  tends  to  fall  back.  It  is  there- 
fore in  the  stable  state  for  unsaturated  air.  If,  however,  this 
initial  force  were  continued  until  the  ascending  current  and  the 
whole  vertical  circulation  were  fully  established,  then  the  tem- 
peratures in  such  an  ascending  current  would  be  those  of  C'  as 
determined  from  Table  III,  allowing  a  decrease  of  5°  between 
the  earth's  surface  and  the  plane  of  incipient  condensation  500* 


VERTICAL    CIRCULATION.  235, 

meters  above.  It  is  seen  that  the  temperatures  now,  from  the 
disengaged  latent  heat  of  condensation,  are  much  greater  than 
those  before  the  ascent  commenced  and  those  of  the  surround- 
ing atmosphere  generally.  If,  therefore,  the  initial  temperature 
disturbance  is  sufficient  to  inaugurate  a  complete  vertical  cir- 
culation, there  is  then  a  tendency  for  it  to  continue  until  this 
tendency  vanishes,  for  reasons  already  given.  If  we  suppose, 
for  reasons  given  in  §  1 56,  that  the  temperature  of  the  interior- 
ascending  air  is  3°  greater  than  that  of  the  surrounding  quiet  air,, 
we  must  add  3°  to  the  temperatures  of  the  columns  B'  and  CV 
and  then,  by  comparing  these  with  A,  it  is  seen  that  not  only  the 
tendency  of  the  air  to  ascend  is  greatly  increased  when  the 
vertical  circulation  is  fully  established,  but  that  there  is  this, 
tendency  as  soon  as  the  air  of  each  stratum  has  ascended  to 
the  plane  of  incipient  condensation  500  meters  above,  and  this 
tendency  after  that  continues  to  increase  until  the  circulation 
is  fully  established. 

161.  Let  us  now  assume  that  the  vertical  distribution  of 
temperature  in  the  atmosphere  over  a  very  large  part  of  the 
earth's  surface  is  that  represented  by  the  column  D  in  the 
preceding  table,  and  that  the  depression  of  the  dew-point,  t  —  d, 
at  all  altitudes  is  8°.  The  air  of  each  very  thin  stratum  in  this 
case  has  to  ascend  about  1000  meters  before  condensation  of 
aqueous  vapor  commences,  and  in  doing  so  is  cooled  down 
10°.  It  then  has  the  temperatures  of  the  column  E,  and  con- 
sequently is  now  much  colder  and  heavier  than  the  surround- 
ing undisturbed  air,  so  that  if  by  any  temporary  impulse  it 
had  received  such  an  upward  motion,  it  would  not  now  tend  to 
go  on  but  to  fall  back,  and  so  in  all  cases  where  the  vertical 
temperature  gradient  is  not  greater  than  that  of  the  indifferent 
state  for  dry  air.  But  if  the  initial  disturbing  force  arising  from 
a  central  higher  temperature  were  sufficient  to  establish  a  com- 
plete vertical  circulation  such  as  to  have  carried  air  from  the 
surface  up  to  high  altitudes,  the  distribution  of  vertical  tem- 
perature now  in  the  ascending  air  would  be  as  represented  by 
the  column  F,  the  whole  ascending  air  having  been  warmed  up- 
by  the  setting  free  of  the  latent  heat  in  condensation  above  its. 


2  36  CYCLONES. 

original  temperatures  of  the  same  altitudes,  instead  of  being 
cooled  below  them  in  the  ascent  through  the  first  1000  meters 
before  condensation  commenced.  The  whole  of  the  ascending 
air  now  is  consequently  warmer  than  that  of  the  surrounding 
parts,  and  has  a  tendency  to  continue  to  rise  up  and  to  main- 
tain the  vertical  circulation.  Such  a  circulation,  however, 
could  not  originate  from  any  slight  disturbance  of  the  atmos- 
phere, as  in  the  case  of  unstable  equilibrium  of  either  dry  or 
fully  saturated  air;  but  it  would  require  that  the  ascending  air, 
^before  ascent,  should  have  a  higher  initial  temperature  than 
that  of  the  surrounding  air  by  about  4°  or  5°,  in  order  that, 
when  it  has  ascended  and  cooled  down  to  the  dew-point,  the 
temperatures  may  be  a  little  greater  than  that  of  the  surround- 
ing air,  at  least  up  to  a  considerable  altitude,  and  not  have 
fallen  below,  and  so  stopped  the  further  ascent  ;  for  if  4°  or  5° 
were  added  to  the  column  E  it  would  make  the  temperatures 
greater  than  those  of  the  column  D  up  to  a  considerable  alti- 
tude, and  so  the  air  would  continue  to  ascend  and  not  fall  back, 
•  and  an  initial  circulation  would  be  established  up  to  at  least  a 
high  altitude.  This  additional  amount  of  temperature  added 
to  the  column  F  indicates  by  comparison  with  D  that  the  force 
by  which  the  vertical  circulation,  when  once  established,  is 
maintained,  would  be  much  increased.  It  is  therefore  possible, 
with  the  preceding  assumed  vertical  temperature  gradient  and 
hygrometric  condition  of  the  air,  for  a  vertical  circulation  of 
the  air  to  originate  and  be  maintained  for  some  time,  provided 
that  the  initial  temperature  disturbance  is  considerable,  and 
not  merely  such  as  to  give  it  a  slight  upward  motion,  as  re- 
quired in  the  cases  of  the  unstable  state  of  the  atmosphere. 

By  comparing  F  with  A  instead  of  with  D,  it  is  seen  that  a 
vertical  circulation  cannot  be  maintained  with  a  depression  of 
the  dew-point  equal  to  8°  with  the  same  condition  of  the  at- 
mosphere with  regard  to  vertical  temperature  gradient  as  in  the 
•case  in  which  the  depression  of  the  dew-point  is  only  4°  ;  for 
in  this  latter  case  the  vertical  circulation  is  kept  up  with  the 
vertical  temperature  gradient  corresponding  to  A,  since  the 
-temperatures  of  C '  which  exist  after  complete  circulation  is 


VERTICAL    CIRCULATION. 

established  are  greater  than  those  of  A,  while  those  of  F,  in  the: 
former  case,  when  complete  circulation  is  established  are  less 
than  those  of  A,  though  greater  than  those  of  D.  Now  the 
longer  the  vertical  circulation  continues,  the  greater  is  the 
depression  of  the  dew-point,  for  as  the  moist  air  ascends  and 
loses  its  moisture  by  condensation,  and  the  surrounding  air 
gradually  descends,  and  the  cold  air  of  the  upper  strata  with 
comparatively  little  aqueous  vapor  comes  down  near  the  earth's 
surface,  the  ascending  current  is  supplied  with  air  which  is 
gradually  becoming  drier,  and  consequently  with  air  having  a 
lower  depression  of  the  dew-point.  It  follows,  therefore,  that  a 
vertical  circulation  which  originates  from  and  is  maintained  by 
a  given  vertical  temperature  gradient  gradually  loses  its  force 
and  finally  vanishes,  because  the  supply  of  air  to  the  ascending 
current  becomes  gradually  drier  and  its  dew-point  lower. 

As  the  dew-point  becomes  lower  and  the  plane  of  incipient 
condensation  and  cloud-formation  rises,  all  the  strata  in  the; 
ascending  current  below  this  are  reduced  to  the  indifferent 
state  for  dry  air,  and  the  slowly  descending  air  in  the  region 
around  is  also  slowly  reduced  to  this  state,  so  that  in  time  the 
whole  atmosphere  in  and  around  the  region  of  ascending  air  is. 
reduced  very  nearly  down  to  the  indifferent  state  for  dry  air, 
and  would  be  entirely  so,  if,  when  the  vapor  is  all  nearly  con- 
densed, the  energy  were  still  sufficient  to  continue  the  circula- 
tion and  it  were  not  broken  up  by  abnormal  disturbances  be- 
fore this  state  is  reached. 

162.  Let  us  now  consider  still  another  temperature  condi- 
tion— one  belonging  to  the  winter  season  with  a  temperature  of 
o°  at  the  earth's  surface,  and  let  us  assume  a  vertical  tempera- 
ture gradient  corresponding  to  the  vertical  distribution  of  tem- 
perature represented  by  the  column  G  in  the  preceding  table, 
and  that  the  depression  of  the  dew-point  is  4°.  Proceeding 
now  as  before,  we  get  for  the  temperatures,  after  the  air  of  the 
different  levels  has  ascended  500  meters,  when  condensation 
commences,  those  contained  in  column  H  ;  and  after  complete 
vertical  circulation  is  established,  approximately  those  of  the 
column  I,  as  accurately  as  they  can  be  conveniently  obtained. 


1238  CYCLONES. 

from  Table  III  by  an  extrapolation  for  the  lower  temperatures. 
By  comparing  H  with  G  it  is  seen  that  when  condensation  first 
commences  the  ascending  air  at  the  higher  altitudes  is  colder 
than  the  surrounding  air,  if  the  ascent  does  not  arise  from  an 
initial  higher  temperature  in  the  ascending  air,  and  that  unless 
this  temperature  is  several  degrees  greater  the  tendency  is  to 
fall  back  after  the  initial  ascent  of  500  meters.  At  lower  levels, 
however,  the  temperature  is  greater  and  the  tendency  is  to 
•continue  on.  If  the  initial  upward  motion  arises  from  a  single 
momentary  impulse,  or  only  a  very  small  difference  of  tempera- 
ture of  the  ascending  air  before  starting,  a  vertical  circulation 
at  first  will  take  place  in  the  lower  strata  only,  and  gradually 
•extend  to  higher  levels ;  but  it  cannot  extend  to  very  high  alti- 
tudes, since  if  such  were  established  we  should  have  the  tem- 
peratures of  the  column  I,  whfch  above  the  altitude  of  5000 
meters  are  less  than  those  of  the  column  G,  and  consequently 
of  the  surrounding  undisturbed  air  at  the  same  levels.  The 
air,  therefore,  would  be  heavier  and  could  not  continue  to  as- 
cend above  that  altitude,  but  would  be  deflected  from  the  cen- 
tral part  outward  in  all  directions  and  descend  slowly  in  the 
•surrounding  regions  toward  the  earth's  surface  without  disturb- 
ing much  the  air  above  at  high  altitudes. 

If  the  air  in  this  case  were  saturated,  the  vertical  circulation 
would  take  place  with  a  smaller  vertical  gradient,  that  is,  with 
smaller  differences  of  temperature  between  the  lower  and  higher 
strata ;  but,  on  the  other  hand,  if  the  air  were  drier  and  the 
depression  of  the  dew-point  were  8°  instead  of  4°,  this  vertical 
gradient  would  have  to  be  larger,  and  the  more  so  the  drier 
the  air  and  the  greater  the  depression,  until  in  the  case  of  per- 
fectly dry  air,  in  order  to  have  a  vertical  circulation,  it  would 
have  to  be  greater  than  that  of  the  indifferent  state  for  dry  air, 
corresponding  to  the  vertical  distribution  of  temperature  given 
in  the  column  K. 

The  relation  between  the  radiation  of  dry  air  and  its  ab- 
sorption of  solar  heat  radiation  is  no  doubt  such  that  the  un- 
stable state  would  be  induced  in  a  dry  atmosphere  after  a  long 
interval  of  perfect  calm  ;  but  in  the  real  atmosphere  of  nature, 


VERTICAL    CIRCULATION.  239 

^containing  more  or  less  of  aqueous  vapor,  we  have  seen  that  this 
state  is  induced  with  a  much  smaller  vertical  temperature  gra- 
dient, and  before  it  approximates  very  nearly  to  that  of  the 
indifferent  state  of  dry  air  vertical  circulations  and  reversions 
take  place,  which  tend  to  bring  it  back  only  partially  to  that  of 
•the  indifferent  state  of  dry  air. 

163.  In  the  first  assumed  cases  in  the  preceding  table,  in 
-which  the  air  at  all  altitudes  is  supposed  to  be  saturated,  con- 
densation takes  place  at  once  at  all  levels,  as  soon  as  an  ascend- 
ing current  is  from  any  cause  induced,  and  the  cloud  or  fog  is 
formed  at  all  altitudes  down  to  the  earth's  surface.  In  the 
second  case,  with  the  same  vertical  gradient  of  temperature, 
rbut  with  a  depression  of  the  dew-point  of  4°,  incipient  conden- 
sation takes  place  at  the  altitude  of  500  meters,  and  the  base 
-of  the  cloud  is  at  that  level ;  but  if  the  depression  of  the  dew- 
point  were  8°,  the  base  of  the  cloud  would  be  at  the  level  of 
1000  meters  above  the  earth's  surface,  supposing  in  all  cases 
that  air  ascends  from  the  surface.  And  in  general  the  height 
>of  the  base  of  the  cloud  is  about  125  meters  for  each  degree  of 
the  depression  of  the  dew-point,  varying  slightly  with  different 
temperatures  and  altitudes  as  is  seen  from  Table  IV.  The 
-drier  the  air,  therefore,  the  higher  are  the  clouds  where  the 
•conditions  are  favorable  to  the  production  of  ascending  cur- 
Brents. 

Without  ascending  currents,  therefore,  there  can  be  no 
clouds ;  and  in  all  the  region  around  that  of  the  ascending  air, 
where  there  is  a  gradual  descent  of  air  to  supply  the  indraught 
of  these  currents,  the  air  is  clear ;  for  if  even  there  were  complete 
saturation  and  cloud  from  a  previous  ascent  of  the  air,  as  it 
began  to  descend  the  air  would  at  once  become  warmer  and 
unsaturated,  and  the  cloud  would  soon  disappear  by  evapora- 
tion. Of  course  it  must  be  understood  here,  as  in  all  that  im- 
mediately precedes,  that  the  air  cools  by  expansion  only.  If 
-the  air  is  cooled  in  other  ways,  as  by  nocturnal  radiation  during 
a  clear  night,  or  by  passing  from  lower  to  higher  latitudes,  or 
from  a  warmer  to  a  colder  surface,  as  from  the  ocean  to  the 
land  in  the  winter,  or  vice  versa  in  summer,  there  may  be  cloud, 


240  CYCLONES. 

called  fog,  at  and  near  the  earth's  surface  without  any  ascent 
of  air  to  higher  altitudes  to  give  rise  to  cooling  by  expansion. 

164.  In  all  of  the  assumed  vertical  temperature  gradients 
of  the  table  of  §  159,  represented  by  the  columns  A,  D,  and  G, 
and  the  assumed  depressions  of  the  dew-point,  it  is  seen,  by 
comparing  these  columns  with  those  of  C,  (7,  F,  and  I,  that 
after  the  ascending  current  is  fully  established,  its  temperature 
in  all  of  these  cases,  up  to  6000  meters,  is  greater  than  that  of 
the  surrounding  air.    It  is  observed,  however,  that  in  the  un- 
disturbed atmosphere  generally,  the  gradient   becomes  much 
smaller  at  great  altitudes,  as  is  seen  in  the  results  obtained 
from  Glaisher's  balloon  ascents  (§  27),  and  instead  of  the  gradi- 
ent being  the  same  at  all  altitudes,  it  diminishes  with  increase 
of  altitude  very  nearly  as  the  pressure  does,  and  consequently 
the  vertical  temperature  gradients  at  very  high  altitudes  be- 
come small.     They  may  be,  and   most  probably  are,  such  that 
the  temperature  of  the  ascending  air  at  high  altitudes  is  less 
and  consequently  the  density  greater  than  that  of  the  surround- 
ing air;  and  so,  even  with  the  momentum  which  it  has  acquired 
in  its  ascent  in  the  lower  strata,  it  does  not  ascend  to  the  top 
of  the  atmosphere,  or  even  to  very  high  altitudes,  but  is  mostly 
or  entirely  deflected  horizontally  in  all   directions  at   a  lower 
level.     In  such  a  case  the  vertical  circulation  would  scarcely,  or 
not  at  all,  extend  to  high  altitudes,  but  be  confined  mostly  to> 
the  lower  strata,  and  the  air  at  very  high  altitudes  be  very  little 
disturbed,  and  this  mostly  or  entirely  by  means  of  friction  be- 
tween it  and  the  air  currents  below. 

If  the  ascending  current  extends  up  to  a  given  level  only, 
of  course  there  is  no  condensation  and  cloud-formation  above 
that  level,  and  the  air  remains  clear  and  comparatively  quiet 
above,  while  below  there  may  be  a  brisk  ascending  current  and 
great  cloudiness. 

165.  We  have  seen  in  preceding  sections,  and  especially  in 
the  examples  given  in  the  table  of  §  159,  that  the  vertical  tem- 
perature gradient  of  the  ascending  air  in  a  cyclone,  and  the 
differences  between  it  and  that  of  the  surrounding  air,  may  be 
and  must  generally  be  very  irregular,  so  that  there   is  not  a 


GYRATORY  MOTION  OF  CYCLONES. 

uniform  horizontal  temperature  gradient  at  all  altitudes  be- 
tween the  interior  and  the  exterior  part,  as  there  is  somewhat 
between  the  equatorial  and  polar  regions  of  each  hemisphere, 
the  differences  of  temperature  here  on  different  parallels,  and 
consequently  the  horizontal  temperature  gradients,  being 
nearly  the  same  at  all  altitudes.  But  still  the  greater  tempera- 
ture in  the  interior  causes  an  upward  expansion  of  the  air  and 
greater  vertical  distances  between  the  isobaric  surfaces  here 
than  in  the  exterior  part  where  the  temperature  is  less,  just  as 
in  the  case  of  the  general  motions  of  the  atmosphere  these  ver- 
tical distances  are  greater  in  the  equatorial  than  in  the  polar 
regions,  as  explained  in  §  71.  The  motions  of  each  part  of  the 
air  between  the  interior  and  the  exterior  are  very  similar  in  the 
two  cases,  except  that  they  are  reversed.  In  the  general  mo- 
tions of  the  atmosphere  the  air  moves  toward  the  pole  or  cen- 
tre above,  descends  gradually  in  the  central  part,  that  is,  in  the 
polar  and  middle  latitudes,  moves  from  the  central  toward  the 
exterior  part  in  the  lower  latitudes  and  ascends  slowly  in  the 
exterior  or  tropical  regions ;  but  where  the  interior  is  the 
warmer,  the  air  moves  toward  the  interior  below,  ascends  in 
the  interior  part,  flows  away  above  toward  the  exterior  part, 
where  it  descends  very  slowly  toward  the  earth's  surface,  there 
to  commence  again  another  circuit.  All  that  is  stated  in  the 
former  case  with  regard  to  neutral  planes  between  the  counter 
horizontal  and  vertical  currents,  the  satisfying  of  the  condition 
of  continuity,  and  the  explanations  of  the  vertical  circulation, 
holds  also  in  this  in  a  general  way.  In  this,  however,  there  is 
not  that  definiteness  of  outer  limit  which  there  is  at  the  equa- 
tor to  each  of  the  hemispheres  in  the  general  hemispheric  cir- 
culation. 

GYRATORY   MOTION  OF  CYCLONES. 

1 66.  We  have  seen  that  while  the  atmosphere  is  clear  and 
somewhat  quiet,  the  tendency  is  for  the  upper  strata  to  cool 
down  to  so  low  a  temperature  in  comparison  with  that  of  the 
earth's  surface  and  the  lower  strata,  that  the  unstable  state  is, 


242  CYCLONES. 

induced,  if  not  for  dry  air,  at  least  in  the  case  of  saturated  air, 
and  that  although  the  air  without  ascending  currents  is  rarely, 
and  only  near  the  earth's  surface  completely,  saturated,  yet  if 
there  is  only  a  slight  local  temperature  disturbance — a  little  ex- 
cess of  temperature  over  some  central  area  above  that  of  the 
surrounding  air — a  vertical  circulation  is  started  which  contin- 
ues until  there  is  such  an  interchange  and  inversion  of  the  air 
of  the  upper  and  lower  strata  that  the  unstable  state  is  de- 
stroyed, and  the  stable  state  and  comparative  calmness  and 
clearness  are  again  restored  for  a  while,  until  broken  up  again, 
in  perhaps  a  short  time,  in  a  similar  manner  as  before.  If  the 
earth  had  no  rotation  on  its  axis  the  air  in  its  vertical  circula- 
tion, in  all  such  cases  of  local  and  temporary  disturbances, 
would  move  in  the  lower  strata  directly  toward  the  central  part 
of  the  area  of  higher  temperature  and  less  pressure  and  out 
from  it  above,  as  already  described,  and  there  would  be  no 
gyratory  motion  around  the  centre.  But  in  consequence  of  the 
earth's  rotation,  where  a  body  moves  in  any  direction  on  the 
earth's  surface  there  is  a  force  which  deflects  it  to  the  right  in 
the  northern  hemisphere,  and  the  contrary  in  the  southern 
(§  53)'  In  the  case  of  a  central  force  acting  upon  the  body,  as 
where  air  is  forced  in  from  all  sides  toward  a  centre  by  a  pres- 
sure gradient,  this  deflecting  force  is  strengthened  by  the  rela- 
tive gyratory  motion  of  the  body  itself,  as  is  seen  from  the  ex- 
pression of  Ft ,  §  52,  in  which  the  part  depending  upon  n  is  due 
to  the  earth's  rotation,  and  that  upon  v  to  the  gyratory  mo- 
tion ;  and  so  very  near  the  centre,  where  v  =  v/r  becomes 
very  large,  the  deflecting  force  becomes  much  greater,  with  the 
same  velocity  of  the  body  s.  The  air  therefore  in  the  lower 
strata,  in  being  forced  in  from  all  sides  toward  the  centre,  runs 
into  a  gyration  around  this  centre,  and  this  in  the  northern 
hemisphere  is  from  right  to  left,  or  contrary  to  the  motion  of 
the  hands  of  a  watch. 

This  may  be  illustrated  by  means  of  the  behavior  of  water 
in  a  shallow  basin,  where  it  is  allowed  to  run  out  through  a 
hole  in  the  centre.  If  the  basin  is  at  rest,  and  the  water  in  the 
basin  has  no  motion  of  any  kind  before  the  hole  is  opened,  the 


GYRATORY  MOTION  OF  CYCLONES.  243 

water  flows  directly  from  all  sides  toward  the  centre,  without 
any  gyratory  motion.  But  if  the  basin,  although  the  water 
with  reference  to  the  basin  is  perfectly  at  rest,  has  the  least 
gyration  around  its  centre,  the  water  in  approaching  toward 
the  centre  runs  into  a  gyration  around  that  centre,  and  the 
gyratory  velocity  becomes  very  great  near  the  centre.  It  is 
somewhat  the  same  where  the  air  over  a  considerable  area  of 
the  earth's  surface  is  forced  from  all  sides  toward  the  centre. 
This  area,  we  have  seen,  §  52,  gyrates,  in  consequence  of  the 
earth's  rotation,  around  its  centre,  with  an  angular  velocity 
proportional  to  the  sine  of  the  latitude ;  and  so  the  air,  in  run- 
ning in  from  all  sides  toward  the  centre,  runs  into  a  gyration 
around  the  centre,  just  as  the  water  in  the  basin.  The  princi- 
pal difference  in  the  two  cases  is,  that  the  water  runs  down 
through  the  hole  and  disappears,  while  the  air  runs  upward 
over  the  central  area,  and  flows  away  above. 

167.  In  the  flowing  away  of  the  air  above  in  all  directions 
from  the  centre,  it  is  deflected  toward  the  right  in  the  north- 
ern hemisphere  by  the  same  force  as  in  running  in  toward  the 
centre.  The  first  effect  is  to  counteract  and  overcome  the  gy- 
ratory velocity  acquired  by  the  air  in  being  forced  toward  the 
centre,  and  after  that  it  produces  a  gyratory  motion  in  the  con- 
trary direction,  that  is,  from  left  to  right.  Where  the  system 
•of  vertical  circulation  and  gyratory  motions  becomes  fully  es- 
tablished, and  the  air  which  flows  out  above  is  drawn  in  again 
toward  the  centre  below,  this  gyratory  motion  from  left  to 
right  has  first  to  be  overcome  by  the  deflecting  force  before  a 
gyratory  motion  from  right  to  left  begins  to  be  generated.  In 
connection,  therefore,  with  every  vertical  system  of  circulation 
there  is  produced  by  the  deflecting  force  of  the  earth's. rotation 
two  kinds  of  gyrations — the  one,  mostly  in  the  interior  part, 
from  right  to  left  in  the  northern  hemisphere,  and  the  other, 
mostly  in  the  exterior  part,  in  the  contrary  direction.  The  in- 
terior, and  by  far  the  most  violent  part,  is  called  a  cyclone,  and 
therefore  the  exterior  and  comparatively  gentle  part  is  prop- 
erly called  an  anti-cyclone ;  and  the  two  always  go  together. 
The  gyrations  of  the  former  are  properly  called  cyclonic  gyr a- 


244  CYCLONES. 

tions,  and  those  of  the  other,  anti-cyclone  gyrations  ;  it  being 
understood  that  each  of  them  is  exactly  reversed  in  the  other 
hemisphere. 

The  deflecting  forces  upon  which  the  gyrations  depend  be- 
ing greatest  at  the  poles  and  diminishing  as  the  sine  of  the  lati- 
tude toward,  and  vanishing  at,  the  equator,  of  course  the  gy- 
rations arising  from  any  given  temperature  disturbance  or  ver- 
tical circulation,  all  other  circumstances  being  the  same,  are 
most  violent  in  the  polar  regions,  less  so  with  decrease  of  lati- 
tude, and  vanish  at  the  equator,  the  motions  there  being  di- 
rectly toward  and  from  the  centre,  the  same  as  would  be  the 
case  everywhere  on  the  earth's  surface  if  the  earth  had  no 
rotation  on  its  axis. 

168.  In  the  case  of  no  friction  between  the  air  and  the 
earth's  surface,  and  the  initial  state  of  the  air  being  that  of 
relative  rest,  each  particle  of  air,  in  being  drawn  in  toward  the 
centre,  would,  after  the  system  of  motions  had  become  fully 
established,  move  in  accordance  with  the  principle  of  the 
preservation  of  areas,  §  41,  provided  we  consider  the  absolute 
gyratory  velocity,  including  both  that  depending  upon  the 
earth's  rotation  and  that  which  is  relative  to  the  earth's  surface. 
Hence,  putting  w  for  the  absolute  gyratory  velocity,  and  r  for 
the  distance  from  the  centre,  we  must  at  all  distances  from  the 
centre  have  the  relation,  as  in  §  42, 


in  which  c  is  a  constant  equal  to  the  average  value  of  rw  taken 
while  the  air  is  yet  at  rest,  and  w  has  the  value  rn't  for  the 
whole  mass  of  air  brought  into  motion.  As  r  diminishes  w 
must  increase,  and  consequently  near  the  centre  it  becomes 
very  great,  and  the  value  there  of  w  consists  mostly  of  the 
gyratory  velocity  relative  to  the  earth's  surface,  since  the  part 
depending  upon  the  earth's  rotation  decreases  as  r,  and  con- 
sequently near  the  centre  becomes  very  small. 

If  each  particle  of  air,  in  being  acted  upon  by  the  centripetal 
force  below,  and  centrifugal  force  above,  arising  from  pressure 
gradients,  were  entirely  free,  not  only  from  the  effect  of  the 


GYRATORY  MOTION  OF  CYCLONES.  245 

friction  of  the  earth's  surface,  but  likewise  from  the  effect  of 
other  particles  acting  upon  it  by  contact  and  by  friction,  its 
gyratory  velocity  would  satisfy  the  preceding  expression  for 
all  values  of  r  or  distances  from  the  centre,  with  the  value  of 
the  constant  c  •=.  r0w0,  in  which  r0  and  w0  were  the  values  of  r 
and  w  before  relative  motion  commenced.  But  since  in  the 
interactions  of  the  different  parts  of  the  air  action  and  reaction 
.are  equal,  these  cannot  affect  the  average  of  rw  for  the  whole 
mass,  and  this,  therefore,  must  remain  constant  and  equal  to 
its  value  before  motion  commenced,  and  therefore  equal  to  the 
average  of  r0w0  for  the  whole  mass.  The  gyratory  velocity  at 
all  altitudes  is  in  this  case  the  same  at  the  same  distances  from 
the  centre,  and  there  is  consequently  no  friction  then  between 
the  strata  arising  from  relative  gyratory  velocities.  The  whole 
deflecting  force  is  spent  in  either  giving  gyratory  velocity  and 
momentum  to  the  air,  or  in  overcoming  this  where  already 
acquired.  The  air,  therefore,  has  a  cyclonic  motion  at  all 
-altitudes  in  the  interior  and  an  anti-cyclonic  motion  in  the 
exterior  part,  and  the  distance  from  the  centre  at  which  the 
cyclonic  changes  to  the  anti-cyclonic  motion  is  the  same  at 
all  altitudes. 

By  referring  to  §  74  it  will  be  seen  that  this  result  is  very 
rsimilar  to  that  in  the  general  motions  of  the  atmosphere  in  the 
case  of  no  friction,  the  value  of  r  being  the  distance  from  the 
centre  of  gyration  in  this,  while  in  the  other  it  is  the  distance 
from  the  earth's  axis  of  rotation. 

169.  If  the  whole  region  of  temperature  disturbance  and 
vertical  circulation,  and  the  underlying  portion  of  the  earth's 
surface,  did  not  have  a  gyratory  motion  around  the  centre  in 
consequence  of  the  earth's  rotation,  the  vertical  circulation 
would  have  the  full  force  due  to  the  pressure  gradients  arising 
from  the  differences  of  temperature  between  the  interior  and 
the  exterior,  as  in  the  case  of  the  general  motions  of  the 
atmosphere  if  the  earth  had  no  rotation  on  its  axis,  and  if 
there  was  no  friction  there  would  be  continued  acceleration  ; 
but  in  case  of  friction  the  acceleration  continues  until  the 
friction  becomes  equal  to  the  forces,  after  which  the  circulation 


246  CYCLONES. 

is  uniform  so  long  as  the  disturbing  forces  are  the  same.  But 
where  the  whole  gyrates  around  the  centre,  we  have  seen,  the 
deflecting  forces  tend  to  produce  a  cyclonic  gyration  in  the 
lower  strata  of  the  atmosphere,  and  an  anti-cyclonic  in  the 
upper  strata ;  but  in  the  case  of  friction  between  the  earth's 
surface  and  the  air,  and  between  the  different  strata  having 
relative  velocities,  the  forces  are  not  entirely  spent  upon  the 
inertia  of  the  air,  as  in  the  case  of  no  friction  (§  168),  but  partly 
upon  the  inertia  and  partly  in  overcoming  the  friction.  So  far 
as  it  is  spent  upon  the  inertia,  the  effect  is  to  cause  cyclonic 
gyrations  in  the  interior  and  anti-cyclonic  gyrations  in  the 
exterior,  as  in  the  case  of  no  friction  between  the  air  and  the 
earth's  surface,  in  which  the  whole  force  is  spent  upon  the 
inertia  of  the  air ;  but  so  far  as  it  is  spent  upon  the  friction 
between  the  different  strata,  the  tendency  is  to  maintain 
counter  gyrations  in  the  lower  and  upper  strata,  cyclonic 
below  and  anti-cyclonic  above.  The  resultant  effect  is,  there- 
fore, in  part  the  one  and  in  part  the  other.  Whatever  the 
gyratory  velocity  below  may  be,  that  above  is  less  for  the 
cyclonic  and  greater  for  the  anti-cyclonic  at  the  same  distances 
from  the  center.  The  greater  the  altitude  of  the  stratum, 
therefore,  the  nearer  the  centre  does  the  change  take  place 
from  the  cyclonic  to  the  anti-cyclonic  gyrations. 

By  comparing  these  results  with  those  obtained  in  a  some- 
what different  manner  with  regard  to  a  whole  hemisphere  in 
the  general  circulation  of  the  atmosphere,  it  will  be  seen  that 
they  are  very  similar,  except  that  in  the  general  circulation  of 
a  hemisphere  the  gyratory  or  east  components  of  velocity  are 
greatest  above,  while  in  the  cyclonic  they  are  least  above ; 
and  in  the  general  circulation  the  distance  from  the  pole  at 
which  the  easterly  velocities  vanish  and  change  to  westerly 
ones  increases  with  increase  of  altitude,  while  in  cyclones  the 
distance  from  the  centre  at  which  the  gyrations  vanish  and 
change  from  the  cyclonic  to  the  anti-cyclonic  decreases  with 
increase  of  altitude.  This  arises  from  the  difference  in  the 
distribution  of  temperature  and  of  the  horizontal  temperature 
gradients  ;  in  the  case  of  the  hemisphere  in  the  general  circu- 


GYRATORY  MOTION  OF  CYCLONES.  247 

lation  the  polar  or  central  region  is  the  colder,  and  in  the 
cyclone  the  central  part  is  the  warmer,  and  consequently  the 
directions  of  the  vertical  circulations  are  reversed  in  the  two 
cases. 

1 70.  Although  in  the  cyclones  the  gyratory  velocities  for 
the  whole  system,  considered  algebraically,  and  regarding  the 
cyclonic  as  the  positive  ones,  are  less  above  than  below,  yet 
there  is  a  limit  beyond  which  the  difference  cannot  go,  and 
this  depends  upon  the  temperature  gradients  between  the 
interior  and  exterior  parts.  As  soon  as  gyratory  motions  are 
produced  there  arises  another  modifying  force,  the  force 
deflecting  to  the  right  of  the  direction  of  gyratory  motion  in 
the  northern  hemisphere  (§  52),  and  so  from  the  centre  in  the 
case  of  cyclonic,  and  toward  it  in  that  of  the  anti-cyclonic 
gyrations.  If  the  gyratory  velocities,  and  consequently  the 
deflecting  forces,  were  the  same  in  the  upper  as  in  the  lower 
strata,  they  would  not  interfere  with  the  vertical  circulation 
which  is  maintained  by  the  gradients  arising  from  differ- 
ences of  temperature,  as  explained  in  §  63,  and  the  vertical 
circulation  would  be  maintained  by  the  full  force  of  the 
pressure  gradients  arising  from  the  differences  of  temperature, 
just  as  in  the  case  of  no  gyrations  whatever.  But  if  these 
deflecting  forces  are  greater  below  than  above,  it  interferes 
with  this  vertical  circulation,  and  the  difference  between  the 
gyratory  velocities  and  the  forces  below  and  above  may  be 
such  as  to  entirely  counteract  the  forces  by  which  the  vertical 
circulation  is  maintained,  just  as  forces  of  different  strengths 
applied  in  the  same  direction  at  the  bottom  and  top  of  a 
turning  wheel,  if  the  difference  is  great  enough,  and  the 
stronger  force  is  applied  in  the  direction  which  tends  to  stop 
it,  entirely  counteracts  the  force  by  which  the  wheel  is  kept  in 
motion. 

In  the  case  of  regular  temperature  gradients,  an  expression 
of  the  differences  of  the  velocities  required  for  this  might  be 
obtained  in  a  function  of  the  temperature  gradient,  as  in  the 
case  of  the  differences  of  the  east  components  of  velocity  above 
and  below  in  the  general  circulation  of  the  atmosphere  (§  77). 


248  CYCLONES. 

But  however  irregular  the  temperature  disturbance  and  the 
temperature  gradients  may  be,  the  differences  between  the 
gyratory  velocities  above  and  at  or  near  the  earth's  surface 
may  be  such  as  to  entirely  destroy  vertical  circulation.  But 
it  is  evident  that  the  actual  differences  must  fall  short  of  this  ; 
for  if  the  gyratory  velocities  were  such  as  to  entirely  stop  ver- 
tical circulation  there  would  then  be  no  deflecting  force  in  a 
direction  at  right  angles  to  that  of  the  vertical  circulation  to 
overcome  the  friction  between  the  strata  having  different  gyra- 
tory velocities,  and  so  this  friction  would  tend  to  reduce  the 
velocities  above  and  below  to  the  same,  and  would  at  once  so 
decrease  the  differences  between  them  that  the  vertical  circula- 
tion would  not  be  entirely  stopped  ;  but  still  its  velocity  would 
be  comparatively  much  smaller  than  in  the  case  of  no  gyration 
of  the  whole  system  around  a  centre,  in  which  cases  the  verti- 
cal circulation  is  not  hindered  by  differences  in  the  deflecting 
forces  below  and  above,  but  the  vertical  circulation  is  main- 
tained by  the  full  force  of  the  pressure  gradients  arising  from 
the  difference  of  temperature  between  the  interior  and  the 
exterior.  These  deflecting  forces,  therefore,  act  as  a  sort  of 
governor,  as  in  the  case  of  the  general  motions  of  the  atmos- 
phere (§  75).  If  the  differences  between  the  gyratory  veloci- 
ties below  and  above,  and  consequently  between  the  deflecting 
forces,  are  a  little  too  great,  the  velocity  of  the  vertical  cir- 
culation becomes  too  small,  and  the  effect  of  this  is  to 
diminish  these  differences,  and  vice  versa. 

Since  the  differences  of  the  velocities  above  and  at  the 
earth's  surface,  in  order  to  counteract  the  vertical  circulation, 
must  be  such  that  the  differences  of  the  deflecting  forces  above 
and  at  the  earth's  surface  are  adequate  to  counteract  the  forces 
by  which  the  vertical  circulation  is  maintained,  and  these  de- 
flecting forces  at  the  same  distance  from  the  centre  are  propor- 
tional to  the  temperature  gradient  there  between  the  interior 
and  exterior  part  of  the  cyclonic  area,  it  is  evident  that  the 
greater  the  temperature  gradients,  the  greater  the  gyratory 
velocities  above  differ  from  those  at  or  near  the  earth's  surface, 
and  very  nearly  or  quite  in  proportion,  since  the  limits  which 


GYRATORY  MOTION  OF  CYCLONES.  249 

they  do  not   reach,  but   fall  short  of   a  very  little,  are  in  that 
proportion. 

But  the  deflecting  forces,  as  seen  from  the  expression  of 
Fv,  §  52,  for  the  same  gyratory  velocity  z/,  increase  as  r  de- 
creases, and  near  the  centre  very  nearly  inversely  as  r,  so  that 
the  relative  velocities  of  the  strata  below  and  above,  required 
to  counteract  the  effect  of  any  given  temperature  gradient, 
are  smaller  the  nearer  the  centre. 

171.  The  conditions  of  temperature  and  of  temperature 
gradients  determine  the  relations  between  the  gyratory  velocities 
above  and  those  near  the  earth's  surface,  whatever  the  latter 
may  be.  These  depend  upon  the  amount  of  frictional  resist- 
ance of  the  earth's  surface  to  the  gyrations  and  upon  the  forces 
which  overcome  these  resistances,  and  must  be  so  adjusted 
that  the  principle  will  be  satisfied  that  all  the  resistances  from 
every  differential  element  of  the  earth's  surface,  so  far  as  the 
gyrations  extend,  multiplied  into  the  distances  from  the  centre, 
or,  in  other  words,  the  sum  of  all  the  moments  of  couple  must 
be  o,  or  else  the  tendency  would  be  to  turn  the  earth  around 
the  axis  the  pole  of  which  is  the  centre  of  the  cyclone.  But 
this  cannot  arise  from  central  forces  alone,  either  centripetal 
or  centrifugal,  such  as  arise  from  the  temperature  gradients, 
and  these  are  the  only  real  forces  concerned,  the  deflecting 
forces,  so  called,  being  simply  modifications  of  the  directions  of 
motion  as  referred  to  the  gyrating  surface  of  the  earth. 

From  the  centripetal  motion  of  the  air  in  the  lower  part  of 
the  atmosphere  arises  the  deflecting  force  which  gives  rise  to  a 
cyclonic  motion,  and  from  the  centrifugal  motion  in  the  upper 
strata,  that  which  counteracts  the  cyclonic  and  tends  to  pro- 
duce an  anti-cyclonic  gyration.  Since  there  must  be  as  much 
motion  toward  the  central  part  below  as  away  from  it  above, 
with  a  slight  exception  while  the  cyclone  is  forming  or  vanish- 
ing, in  order  to  satisfy  the  condition  of  continuity,  these  de- 
flecting forces  are  exactly  equal  and  contrary  to  each  other, 
•and  so,  taken  together,  have  no  tendency  to  overcome  the 
friction  between  the  air  and  the  earth's  surface  in  the  cyclonic' 
-and  anti-cyclonic  gyrations,  but  tend  mostly,  after  the  vertical 


250  CYCLONES. 

and  gyratory  circulations  are  fully  established,  to  overcome  the- 
friction  between  the  strata  of  air  having  different  gyratory 
velocities,  and  in  part  to  change  the  gyratory  moments.  Be- 
fore that,  of  course,  especially  at  first,  the  forces  are  mostly 
spent  in  overcoming  the  inertia  of  the  air  in  producing  or  de- 
stroying these  moments.  As  the  air  which  moves  in  toward 
the  centre  below  has  a  greater  gyratory  velocity  than  it  has  at 
the  same  distance  from  the  centre  in  flowing  out  above,  the 
air,  from  the  time  it  enters  below  within  a  given  distance  of  the 
centre  until  it  passes  out  above  beyond  that  distance,  loses  a 
certain  amount  of  kinetic  energy  corresponding  to  the  differ- 
ence of  gyratory  velocities  at  the  times  of  entering  within,  and 
passing  without,  this  limit  ;  and  this  amount,  meanwhile,  has. 
been  spent  upon  the  frictional  resistance  of  the  earth's  surface 
within  the  given  distance  from  the  centre.  A  part  of  the  de- 
flecting force  above  is  spent  in  decreasing  the  gyratory  velocity 
there,  and  consequently  only  what  is  left  counteracts,  through 
friction  between  the  strata,  the  equal  deflecting  force  in  the 
contrary  way  below,  and  the  remainder  not  counteracted  is  left 
to  overcome  the  friction  at  the  earth's  surface,  but  this  is  equal 
to  that  arising  from  the  gradual  loss  of  the  kinetic  energy. 

We  have  just  seen  that  the  relative  velocities  of  the  gyra- 
tions above  and  below  decrease  directly  as  the  radial  temper- 
ature gradients,  and  also  decrease  with  the  decrease  of  r,  the 
distance  from  the  centre,  but  not  in  proportion.  But  the 
temperature  gradient  vanishes  at  the  centre,  and  must  be  very 
small  for  some  distance  near  the  centre.  The  amount  of  mo- 
mentum lost,  therefore,  as  the  air  ascends  to  higher  altitudes, 
and  consequently  the  force  upon  which  the  gyratory  velocity 
at  the  earth's  surface  is  maintained,  is  very  small  near  the 
centre,  and  consequently  the  gyratory  velocity  there  is  com- 
paratively small,  where  there  are  frictional  resistances  to  be 
overcome,  though  where  there  are  no  such  resistances  they 
become  greater  very  nearly  inversely  as  the  distance  from  the 
centre. 

In  the  exterior  part  of  the  cyclonic  system,  where  the  gy- 
rations at  the  earth's  surface  are  anti-cyclonic,  it  is  readily  seen?. 


ATMOSPHERIC  PRESSURE  IN  CYCLONE-S.  2$l 

how  the  air  in  the  upper  strata,  where  it  has  a  greater  anti- 
cyclonic  gyratory  velocity,  in  settling  down  gradually  into  the 
lower  strata  in  its  vertical  circulation,  where  the  gyratory  ve- 
locity is  less,  gradually  loses  its  momentum,  and  that  this  lost 
momentum,  by  means  of  friction,  is  transferred  to  the  surface, 
where  it  becomes  a  force  applied  directly  to  overcoming  the 
frictional  resistance  to  the  anti-cyclonic  gyrations. 

172.  The  gyratory  velocities  at  the  earth's  surface  corre- 
sponding to  the  frictional   resistances  which  are  equal   to   the 
forces  overcoming  them,  of  course  depend  upon  the  nature  of 
the  surface  and  the  law  of  resistance  with   regard  to  different 
velocities.     For  a  homogeneous  surface,  however,  whatever  this 
law,  it  is  evident  that  the  velocities  of  the  cyclonic  gyrations 
must,  upon  the  whole,  be  much  greater  than  those  of  the  anti- 
cyclonic,  in  order  to  have  the  sums  of  the  moments  of  couple 
equal,  since  the  former  are  much  nearer  the  centre,  unless  the 
cyclonic  gyrations  cover  a  much  larger  area.     But  this  is  not 
the  case,  but  rather  the  contrary  ;  for  the  whole  cyclonic  area 
having  no  definite  limit,  the  anti-cyclonic  part  is  spread  over  a 
much  larger  area,  and  therefore  the  gyratory  velocities  are  very 
small  in  comparison  with  those  of  the  interior  cyclonic  part. 

The  less  the  amount  of  frictional  resistance  at  the  earth's 
surface  corresponding  to  any  given  gyratory  velocity,  the 
greater  the  gyratory  velocities,  so  that  at  sea,  with  a  smooth 
surface,  the  gyrations,  with  the  same  amount  of  energy  spent, 
are  greater  than  on  land.  And  in  the  case  of  no  such  fric- 
tional resistances,  as  we  have  seen,  they  would  become  very 
great  near  the  centre,  the  principle  of  the  preservation  of  areas 
being  satisfied  in  this  case,  and  the  whole  deflecting  force  in 
this  case  would  act  in  overcoming  the  inertia  of  the  air  and 
producing  gyratory  momentum  as  it  proceeds  toward  the 
centre  in  the  cyclonic  part,  and  in  overcoming  this  momentum 
as  the  air  flows  back  from  the  centre. 

ATMOSPHERIC    PRESSURE    IN    CYCLONES. 

173.  Whatever  the  nature  of  the  earth's  surface  and  the 
gyratory  velocities  there,  it  has  been  shown  that  the  differences. 


252  CYCLONES. 

between  these  velocities  and  those  at  any  altitude  above  at  the 
same  distance  from  the  centre  are  the  same  in  any  case,  so  that 
where  the  gyratory  velocities  at  the  earth's  surface  are  greater 
for  any  reason,  all  those  at  any  altitudes  above  are  increased 
by  the  same  amount.  This  however  must  be  taken  in  an  alge- 
braic sense  toward  the  outer  limit  of  the  cyclonic  part  at  the 
earth's  surface,  where  the  cyclonic  gyrations  below  change  to 
the  anti-cyclonic  above ;  that  is,  an  increase  of  the  cyclonic 
•velocities  below  diminishes  the  anti-cyclonic  gyratory  velocities 
-above.  If  we  imagine  the  resistances  at  the  earth's  surface  to 
be  so  great  that  there  are  sensibly  no  gyratory  velocities  there, 
then  the  same  differences  will  exist  between  these  and  the 
gyratory  velocities  above,  now  all  anti-cyclonic,  and  these  are 
.such  as  to  approximate  very  nearly  to  that  limit  at  which,  by 
means  of  the  deflecting  force  toward  the  centre,  the  air,  ex- 
panded upward  by  a  higher  temperature  in  the  interior  than 
the  exterior  part  of  the  whole  area  of  cyclonic  disturbance,  is 
completely  hindered  from  flowing  away  above  from  the  interior 
to  the  exterior  part.  It  has  been  explained  that  the  differ- 
ences between  the  gyratory  velocities  below  and  above  must  fall 
a  little  short  of  this  limit  so  as  to  allow  a  little  vertical  circu- 
lation, and  consequently  small  gradient  of  decreasing  pressure 
toward  the  centre  at  the  earth's  surface  to  keep  up  this  circu- 
lation, as  explained  in  §  63.  The  pressure,  therefore,  at  the 
earth's  surface  is  scarcely  affected  by  the  upward  expansion  of 
air  in  the  interior  from  a  higher  temperature,  since  the  anti- 
cyclonic  gyrations  almost  entirely  prevent  its  flowing  away 
above,  and  the  consequent  diminution  of  the  pressure  at  the 
earth's  surface. 

All  the  other  conditions  remaining  the  same,  if  we  now 
suppose  that  there  are  gyratory  velocities  at  the  earth's  surface, 
then  all  the  velocities  at  all  altitudes  are  changed  by  the  same 
^amount,  taken  algebraically  when  the  gyrations  change  with 
change  of  altitude  from  positive  to  negative,  that  is,  from  cy- 
clonic to  anti-cyclonic,  or  the  reverse.  Hence  the  pressure 
gradients  change  by  the  same  amount  proportionally  at  all  alti- 
tudes, and  the  pressure  gradient  at  the  earth's  surface,  depends 


ATMOSPHERIC  PRESSURE  IN  CYCLONES.  2$$ 

simply  upon  the  gyratory  velocity  at  the  surface,  with  the  ex- 
ception of  the  small  gradient  referred  to  above,  sufficient  to 
overcome  the  friction  of  the  centripetal  flow  below. 

The  method  of  obtaining  the  barometric  gradient  corre- 
sponding to  any  given  gyratory  velocity  by  means  of  Table  V, 
has  been  explained  in  §  57.  If,  in  connection  with  the  gyratory 
velocity,  there  is  a  component  of  velocity  toward  or  from  the 
centre,  then  the  gradient  required  to  maintain  this  velocity, 
must  be  added. 

Since  the  barometric  gradient  is  proportional  to  the  hori- 
zontal force  which  causes  it,  and  this,  as  we  have  seen,  depends 
almost  entirely  upon  the  gyratory  velocities,  then  it  follows 
from  the  expression  of  this  force,  Fv  in  §  52,  that  near  the 
centre  of  the  cyclone,  where  r  is  small,  and  consequently  v  =  v/r 
is  large,  that  this  gradient  is  very  steep  in  comparison  with 
what  it  is  for  the  same  gyratory  velocity  v  at  a  distance  from 
the  centre,  where  r  is  comparatively  large.  But  v  also  is  largest 
somewhere  near  the  centre,  and  consequently  the  gradients 
here  are  comparatively  very  steep. 

For  instance,  suppose  on  the  parallel  of  40°  we  had  in  the 
anti-cyclonic  part  a  gyratory  velocity  of  20  meters  per  second 
at  the  distance  of  2000  kilometers.  From  Table  V  we  have 
o.ioio  X  20  =  2.02  for  the  gradient  of  pressure  increasing  to- 
ward the  centre.  But  this  must  be  decreased  by  the  centrifu- 
gal force  of  curvature,  since  here  the  two  forces  are  in  con- 
trary directions,  in  the  ratio  of  v/r  —  20/2,000,000  =  o.ooooi  to 
2  n  sin  /  =  0.0000917,  by  Table  V,  or  1/9  very  nearly.  In  the 
cyclonic  part,  at  the  distance  of  200  kilometers,  the  part  of  the 
gradient  of  pressure  increasing  in  a  direction  from  the  centre 
due  to  the  earth's  rotation  is  the  same  as  before,  but  now  the 
centrifugal  force  is  10  times  as  much  as  in  the  other  case,  and 
is  in  the  same  direction  as  the  other.  We  therefore  have  in  this 
case  the  gradient  G  —  2.02  +  2.02  X  10/9  =  4.26.  Still  nearer 
the  centre,  with  the  same  gyratory  velocity,  the  gradient,  it  is 
readily  seen,  would  be  still  much  steeper.  The  gradient  there- 
fore, in  the  anti-cyclonic  part,  even  in  this  case,  is  small  in  com- 
parison with  what  it  is  near  the  centre,  but  the  gyratory  velocity 


:254  CYCLONES 

in  the  anti-cyclonic  part,  we  have  seen,  is  also  much  smaller, 
and  so  for  both  these  reasons  it  is  always  comparatively  small 
here. 

174.  Since  the  deflecting  forces  of  the  cyclonic  and  the 
anti-cyclonic  gyrations  are  from  the  centre  in  the  former,  and 
.toward  it  in  the  latter,  the  greatest  pressure  is  at  the  distance 
from  the  centre  where  they  vanish  and  change  from  the  one 
to  the  other,  at  least  so  far  as  the  pressure  and  pressure  gra- 
dients depend  upon  these  forces.  The  difference  of  pressure 
between  the  lowest  at  the  centre  and  the  highest  where  the 
•gyrations  vanish,  depends  of  course  upon  the  summation  of  the 
pressure  gradients,  and  as  these  are  comparatively  sttep  in  the 
•cyclonic  part,  the  difference  between  the  highest  pressure  and 
that  at  the  centre  is  generally  very  much  greater  than  that  in 
the  anti-cyclonic  part  between  the  highest  pressure  and  that  of 
the  general  undisturbed  surrounding  pressure. 

What  has  just  been  stated  with  regard  to  pressures  at  the 
•earth's  surface  is  true  of  those  at  any  altitude  above  the  sur- 
face. For  the  atmosphere  above  any  given  level  can  be  re- 
garded as  a  separate  atmosphere,  and  the  gyratory  velocities 
of  the  general  atmosphere  at  that  level  as  those  of  the  base  of 
the  atmosphere  above  that  level.  At  any  given  altitude, 
therefore,  the  highest  pressure  in  the  plane  of  that  altitude  is 
also,  or  very  nearly,  where  the  gyrations  vanish  and  the  cy- 
clonic change  into  the  anti-cyclonic.  But  the  greater  the  alti- 
tude the  nearer  the  centre,  as  we  have  seen,  does  this  change 
take  place,  and  the  conditions  maybe  such  that  at  considerable 
.altitudes  the  gyrations  may  be  anti-cyclonic  at  all  distances  from 
the  centre,  and  in  this  case  there  is  no  central  area  of  low 
pressure,  but  the  greatest  pressure  is  in  the  centre,  and  the 
gyrations  are  all  anti-cyclonic ;  and  considering  the  part  of  the 
atmosphere  above  this  level,  we  have  here  an  anti-cyclone  alone, 
with  no  interior  cyclone,  while  at  lower  levels,  the  gyrations 
are  partly  cyclonic,  and  partly  anti-cyclonic,  the  former  increas- 
ing and  the  latter  decreasing  in  area,  and  the  barometric  de- 
pression in  the  centre  becoming  deeper  as  the  altitude  is  di- 
minished, until  we  reach  the  earth's  surface. 


RESULTANT  MOTIONS. 

All  that  area  in  a  cyclone  in  which  the  barometric  pressure 
is  below  the  usual  average,  say  30  inches  or  760  mm.,  is  called 
an  area  of  low  pressure.  It  is  evident  that  the  depth  of  the 
minimum  pressure  depends  both  upon  the  extent  of  the  area 
and  the  gradients  at  the  different  distances  from  the  centre. 
Where  the  gyratory  velocity  is  very  great  near  the  centre,  the 
gradient  depends  almost  entirely  upon  the  centrifugal  force, 
especially  in  low  latitudes,  and  as  this  becomes  very  great 
where  the  radius  is  small,  such  cyclones,  even  if  of  small  extent, 
-may  have  a  deeper  minimum  pressure  than  large  cyclones. 

RESULTANT    MOTIONS. 

175.  Since  the  motions  of  the  air  in  a  cyclone  consist  of 
both  a  vertical  and  gyratory  circulation,  the  resultant  at  any 
place  depends  upon  both  of  these  motions  as  rectangular 
•components,  and  hence  the  direction  of  motion,  upon  the  rela- 
tions of  these  components.  In  the  lower  part  of  the  atmos- 
phere the  horizontal  motion  of  the  vertical  circulation  of  the 
air  is  mostly  from  the  exterior  toward  the  centre,  and  hence 
here  in  both  the  cyclonic  and  anti-cyclonic  parts  of  the  system, 
•the  resultant  direction  inclines  from  the  tangent  of  gyratory 
motion  in  toward  the  centre,  and  the  angle  between  this  tan- 
gent and  the  resultant  direction  is  called  the  inclination.  But 
in  the  upper  part  of  the  atmosphere,  above  the  neutral  plane, 
where  there  is  no  interchanging  motion  between  the  interior 
and  the  exterior  of  the  area  of  cyclonic  disturbance,  the  motion 
is  outward,  and  hence  the  resultant  direction  deviates  toward 
the  exterior  from  the  tangent,  and  the  inclination  in  this  case  is 
negative  or  outward.  In  the  neutral  plane,  of  course,  there  is 
no  inclination,  and  the  only  component  of  motion  here  is  that 
-of  gyratory  motion. 

Since  the  horizontal  component  of  the  motion  of  the  air, 
in  its  vertical  circulation,  is  gradually  retarded  as  the  air  ap- 
proaches the  centre  of  the  cyclone,  and  becomes  o  at  the  cen- 
tre, and  small  even  at  a  considerable  distance  from  the  centre, 
while  the  gyratory  component  of  motion  here  is  usually  large, 


256  CYCLONES. 

the  inclination  of  the  resultant  or  cyclonic  motion  near  the 
centre  is  small  in  comparison  with  what  it  is  in  the  outer  part 
of  the  area  of  violence  and  of  the  cyclone  proper,  and  so  much 
more  nearly  circular. 

At  and  near  the  earth's  surface,  just  beyond  the  ring  of 
highest  pressure,  there  is  an  exception  to  the  inclination  toward 
the  centre.  In  consequence  of  the  anti-cyclonic  gyratory  mo- 
tion being  retarded  here  by  the  greater  amount  of  friction,  the 
deflecting  force  toward  the  centre  here  is  so  much  weakened 

o 

that  it  is  not  equal  to  that  of  the  pressure  gradient,  and  the 
air,  instead  of  flowing  in  toward  the  centre,  is  forced  out  in  the 
contrary  direction  from  beneath  the  high  pressure.  Hence 
here  the  resultant  direction  is  anti-cyclonic  and  outward  and 
the  inclination  negative,  as  in  the  upper  part  of  the  atmos- 
phere. 

On  the  other  side  of  the  ring  of  highest  pressure  the  ten- 
dency, for  the  same  reason,  is  for  the  air  to  be  forced  out  from 
beneath  toward  the  centre,  and  consequently  this  force  com- 
bines with  that  of  the  general  gradient  near  the  surface  arising 
from  differences  of  temperature,  upon  which  the  vertical  circu- 
lation depends,  and  so  increases  this  component  of  motion 
very  much,  and  causes  the  inclination  here  to  be  much  greater 
than  it  otherwise  would  be,  and  also  greater  than  that  in  the 
higher  strata  immediately  above. 

On  both  sides  of  the  ring  of  highest  pressure  the  gyrations 
are  strengthened  by  the  outflow  of  air  beneath  on  each  side, 
for  the  deflecting  force  depending  upon  the  earth's  rotation  aris- 
ing from  this  outflow  is  in  both  cases  in  the  right  direction  for 
this.  In  fact,  on  the  outside  of  this  ring  there  could  be  no 
anti-cyclonic  gyration  if  it  were  not  for  this  force. 

176.  We  have  seen  that  if  it  were  not  for  the  viscosity  of 
the  air,  the  relative  gyratory  velocities  below  and  above  would 
be  such  that  all  vertical  circulation  would  be  prevented,  and 
so  in  this  case  all  the  conditions  of  the  problem  would  be  sat- 
isfied with  a  gyratory  motion  simply,  whatever  these  may  be 
at  the  earth's  surface.  But  with  the  least  viscosity,  the  ten- 
dency is  to  reduce  these  relativeve  locities  to  o,  unless  there  is 


SURFACE    CALMS.  2$? 

a  little  vertical  circulation  sufficient  to  give  rise  to  deflecting 
forces,  in  the  one  direction  below  and  the  contrary  above,  suf- 
ficient to  overcome  the  friction  which  tends  to  diminish  these 
relative  velocities.  The  less  the  friction,  therefore,  due  to  vis- 
cosity, between  strata  of  air  moving  with  different  velocities, 
the  less  of  the  vertical  circulation  is  required.  The  less  the 
friction,  therefore,  the  less  the  inclination  of  the  resultant  mo- 
tion, this  entirely  vanishing  where  there  is  no  friction.  Hence 
near  the  earth's  surface,  where  there  is  much  friction,  there  is  a 
larger  inclination,  while  in  the  upper  strata  it  is  comparatively 
small  and  the  gyrations  are  more  nearly  circular. 

It  must  not  be  understood,  however,  that  this  is  true  ii> 
general  for  all  parts  of  the  system,  but  only  at  any  given  place ; 
for  the  inclination  depends  upon  the  condition  of  continuity 
and  other  conditions.  For  instance,  near  the  centre  there  is  a 
tendency  of  the  air  to  run  into  rapid  gyrations,  while  the  veloc 
ity  of  the  inflow  of  air  toward  a  centre,  or  any  barrier  by  which 
it  is  stopped,  must  gradually  become  less  and  less  and  finally 
vanish.  Near  the  centre  of  a  cyclone,  therefore,  the  ratio  be- 
tween the  radial  and  the  gyratory  velocity,  and  consequently 
the  inclination,  is  in  general  less  than  at  greater  distances. 

SURFACE   CALMS. 

177.  It  has  been  shown  (§  171),  that  near  the  centre  of  a 
cyclone  the  force  which  tends  to  keep  up  a  gyratory  motion 
becomes  very  small.  There  is,  therefore,  little  or  no  motion 
of  that  sort  for  some  distance  from  the  centre.  But  we  have 
just  seen  above  that  the  motion  to  or  from  the  centre  also  be- 
comes small  near,  and  vanishes  at,  the  centre.  However  vio- 
lent the  gyrations  of  a  cyclone,  therefore,  may  be  at  some  dis- 
tance from  the  centre,  at  and  near  the  centre  there  is  always 
sensibly  a  calm,  extending  to  greater  or  less  distances,  accord- 
ing to  the  dimensions  of  the  cyclone  and  other  circumstances. 

Under  the  ring  of  highest  pressure  there  is  no  gyratory 
motion,  for  we  have  seen  that  the  gyratory  velocities  must 
necessarily  vanish  and  change  sign  at  some  distance  from  the 


258  CYCLONES. 

centre,  and  it  has  been  shown  that  here  is  the  place  where 
there  is  the  highest  pressure.  And  as  the  air  also  flows  out 
from  beneath  this  highest  pressure,  on  the  one  hand  toward  the 
interior  and  on  the  other  toward  the  exterior,  it  is  evident  that 
there  is  here  no  radial  motion.  There  being,  therefore,  neither 
gyratory  nor  radial  motion,  there  must  be  here  a  ring  of  calms. 
But  on  account  of  the  very  small  gyratory  velocities  (§  174) 
and  consequent  pressure  gradients  at  the  earth's  surface  in  the 
anti-cyclone,  as  compared  with  those  of  the  cyclone,  and  also 
because  here  the  radial  velocity  depends  upon  the  differences 
between  two  forces,  the  one  arising  from  the  temperature  and 
resulting  pressure  gradient,  which  tends  to  keep  up  the  vertical 
circulation,  and  the  other  arising  from  the  tendency  to  flow  out 
from  beneath  the  high  pressure,  the  motions  of  the  air  at  the 
earth's  surface  in  the  anti-cyclone  are  very  gentle,  and  generally 
of  about  the  same  order  as  the  various  abnormal  disturbances 
and  irregularities,  so  that  they  are  not  readily  distinguished  by 
observation  ;  but  that  such  anti-cyclonic  and  outward  motions 
do  exist,  and  a  corresponding  pressure  gradient,  with  a  maxi- 
mum pressure  at  some  intervening  distance  between  the  centre 
and  exterior  limit,  is  without  doubt. 

GRAPHIC   REPRESENTATION   OF   MOTION   AND   PRESSURE. 

178.  In  Fig.  I  is  given  a  graphic  representation  of  the  re- 
sultant motions  and  of  the  barometric  pressures  for  both  the 
surface  of  the  earth  and  for  some  level  high  up  in  the  atmos- 
phere and  above  the  neutral  plane,  where  the  motions  in  the 
vertical  circulation  are  outward  from  the  centre.  The  solid 
circles  represent  isobars  at  the  earth's  surface  and  the  solid 
arrows  the  directions,  and  in  some  measure,  by  their  different 
lengths,  the  relative  velocities  of  the.  wind.  The  heavy  circle 
represents  the  circle  of  greatest  barometric  pressure  at  the 
earth's  surface,  say  765  mm,,  while  the  pressure  of  the  outer 
border  is  760  mm.,  and  the  dividing  line  between  the  cyclonic 
and  anti-cyclonic  gyrations.  Within  this  limit  the  pressure 
diminishes  to  the  centre  and  the  gyrations  are  cyclonic  and 


•GRAPHIC  REPRESENTATION  OF  MOTION  AND  PRESSURE.  259 

the  direction  -of  the  resultant  of  motion  inclines  in  toward  the 
centre,  but  beyond  that  limit  the  gyrations  are  anti-cyclonic 
and  the  direction  of  resultant  motion  inclines  toward  the  outer 
border  of  these  gyrations.  The  heavy  dotted  circle  represents 
the  circle  of  maximum  pressure  at  some  high  level,  and  is  much 
nearer  the  centre  than  that  at  the  earth's  surface.  It  is  also 


Fig.  I. 

the  dividing  line  between  the  cyclonic  and  anti-cyclonic  gyra- 
tions at  that  level.  The  dotted  arrows  indicate  the  directions, 
.and  in  some  measure  the  relative  velocities,  of  the  wind  at  this 
level.  The  arrows  in  the  cyclonic  part  represent  the  direction 
of  the  wind  as  declining  outward,  because  the  plane  here  con- 
sidered is  supposed  to  be  above  the  neutral  plane,  where  the 
•radial  component  of  motion  is  outward,  but  for  any  level  be- 


26O  CYCLONES. 

low  the  neutral  plane  the  inclination  is  still  inward.  The 
arrows  are  shorter  above  in  the  cyclonic  part  and  longer  in  the 
anti-cyclonic  part  than  they  are  at  the  earth's  surface,  since  the 
cyclonic  gyratory  velocities  decrease  and  the  anti-cylonic  in- 
crease with  increase  of  altitude. 

The  upper  part  of  the  figure  is  a  representation  of  a  verti- 
cal section  of  the  air,  very  much  exaggerated  in  altitude,  in 
which  the  solid  curved  line  represents  a  section  of  an  isobaric 
surface  near  the  earth's  surface,  say  of  740  mm.  barometric 
pressure.  The  lowest  part  corresponds  with  the  centre  of  the 
cyclone  and  the  highest  part  with  the  heavy  circle  in  the  lower 
part  of  the  figure,  and  the  steepest  gradients  with  the  longest 
solid  arrows,  since  the  greater  the  gyratory  velocities  at  the 
earth's  surface  the  greater  the  gradients,  though  they  are  not 
strictly  proportional.  The  second  dotted  curved  line  from  the 
top  represents  a  section  of  the  isobaric  surface  of  high  altitudes, 
in  which  the  highest  parts  correspond  with  the  heavy  dotted 
circle  below,  since  the  highest  pressure  at  all  altitudes  is  very 
nearly  where  the  cyclonic  gyrations  vanish  and  change  to  the 
anti-cyclonic.  The  depression  here  is  smaller  because  the 
cyclonic  area  is  smaller,  and  the  gyratory  velocities  less,  than 
at  the  earth's  surface.  The  upper  dotted  line  belongs  to  an 
isobaric  surface  still  higher,  where  the  gyrations  are  supposed 
to  be  all  anti-cyclonic,  and  here,  consequently,  the  greatest 
pressure  is  in  the  centre,  as  indicated  by  the  curved  line. 

As  the  interior  of  the  whole  cyclonic  system  is  warmer 
than  the  exterior,  and  consequently  the  air  less  dense,  the  dis- 
tances between  the  isobaric  surfaces  are  necessarily  greater  in 
the  interior  than  the  exterior  part,  and  so,  however  much  the 
isobaric  surface  at  or  near  the  earth's  surface  may  be  depressed 
by  the  cyclonic  gyrations  there,  at  a  considerable  altitude,  if 
the  temperature  difference  is  great  enough,  it  must  become 
convex  instead  of  concave. 

The  track  of  any  given  particle  of  air  in  a  cyclone,  resulting 
from  the  vertical  and  gyratory  circulation,  is  that  of  a  large 
converging  and  ascending  spiral  in  the  lower  part,  but  of  a 
diverging  and  ascending  spiral  in  the  upper  strata  of  the  at- 


COMPARISONS    WITH  OBSERVATIONS.  26 1 

mosphere,  and  the  nearer  the  earth's  surface  the  more  nearly 
horizontal  is  the  motion,  since  the  vertical  component  gradu- 
ally decreases  and  vanishes  at  the  surface. 

The  whole  energy  of  the  system  by  which  the  inertia  of  the 
.air  and  the  frictional  resistances  are  overcome  and  the  motions 
maintained,  is  in  the  greater  interior  temperature  and  the  tem- 
perature gradients,  by  which  the  circulation  is  maintained. 
This  being  kept  up,  the  deflections  and  gyrations  are  merely  the 
result  of  the  modifying  influence  of  the  earth's  rotation,  which 
is  not  a  real  force,  since  it  does  not  give  rise  to  kinetic  energy, 
;but  merely  to  changes  of  direction. 

It  must  be  borne  in  mind  that  the  preceding  is  a  represen- 
tation of  the  motions  and  pressures  of  a  cyclone  resulting  from 
perfectly  regular  conditions,  in  an  amosphere  otherwise  undis- 
turbed, and  having  a  uniform  temperature,  except  so  far  as  it 
is  affected  by  the  temperature  disturbance  arising  from  the 
cyclonic  conditions.  Accordingly  results  so  regular  are  not  to 
be  found  in  nature,  but  generally  only  rough  approximations 
to  them. 

Since  the  wind  inclines  less  and  less  toward  the  centre  of  the 
•cyclone  below  the  neutral  plane  and  declines  from  the  centre 
above  it,  the  upper  currents  above  this  plane  in  a  cyclone  are 
always  from  a  direction,  in  the  northern  hemisphere,  a  little 
to  the  right  of  that  of  the  lower  currents,  when  not  affected  by 
abnormal  circumstances. 

COMPARISONS  WITH   OBSERVATIONS. 

179.  All  the  phenomena,  as  deduced  from  theoretical  con- 
siderations, have  been  confirmed  by  observation.  Areas  of 
low  pressure  with  encircling  winds,  properly  called  cyclonic 
depressions,  are  constantly  occurring  in  nearly  all  parts  of  the 
world,  and  their  delineations  on  the  charts  of  the  different 
Weather  Bureaus  are  familiar  to  many  persons.  A  remarkable 
example  of  this  kind  has  been  recently  given  by  Mr.  Harding3 
of  the  storm  which  swept  across  the  British  Islands  on  Decem- 
ber 8th  and  Qth,  1886,  and  which  was  one  of  the  most  violent  dis- 


262 


CYCLONES. 


turbance  swhich  had  occurred  for  many  years.  The  following* 
figure  is  a  copy  of  his  chart  given  for  6  P.M.  of  the  8th  so  far 
as  observations  were  available.  From  this  it  is  seen  that  the 
barometric  depression  in  the  centre  is  more  than  two  inches,, 
and  that  the  gradients,  especially  on  the  southeasterly  side,  are 
very  steep,  indicating  very  strong  winds.  The  arrows  indicate 
that  the  motion  of  the  air  is  cyclonic  around  the  lowest  press- 
ure with  an  inclination  toward  the  centre. 

On  the  southeasterly  side  the  difference  of  the  barometer 
was  I  inch  in  240  miles,  giving  a  gradient  of  about  7  mm.     The 

greatest  observed  velocities  were 
over  70  miles  per  hour,  giving 
a  gyratory  velocity  a  little  less 
of  about  30  m.  per  second,  and 
these  most  probably  correspond^ 
ed  very  nearly  with  the  preced- 
ing gradient.  A  straight-lined 
wind  on  the  parallel  of  50°  with 
a  velocity  of  30  meters  per  sec- 
ond, by  Table  V,  would  give  a 
gradient  G  —  0.1204  X  30  =  3.6 
mm.,  and  consequently  would 
not  nearly  give  the  observed 
gradient  of  7  mm.  But  if  we 
suppose  the  gyration  had  a  ra- 
dius of  curvature  of  400  kilome- 


Fig.  2. 


ters,  then,  as  explained  in  §  173,  this  gradient  is  increased  from 
this  cause  by  a  quantity  which  is  to  it  in  the  ratio  of  30/400000 
to  2  n  sin  /=  .00009,  by  Table  V,  and  so  by  a  quantity  equal 
3.0  mm.  The  gradient,  therefore,  with  this  radius  of  curva- 
ture becomes  6.6  mm.,  very  nearly  equal  to  the  observed  gradi- 
ent. But  to  this  a  small  unknown  addition  has  to  be  made  for 
the  pressure  gradient  resulting  directly  from  the  temperature 
gradient. 

180.  The  inclination  of  the  winds  at  the. earth's  surface  in  a 
cyclone  was  observed  by  Redfield  in  the  great  cyclones  which 
originate  within  the  tropics  and  progress  northward  and  north- 


COMPARISONS    WITH  OBSERVATIONS.  263 

eastward  to  the  higher  latitudes,  but  no  estimates  were  made 
of  the  average  angle  of  inclination. 

Soon  after  this  Dr.  Buys  Ballot  gave  his  law,  of  more  general 
application,  namely,  that  winds  always  blow,  in  the  northern 
hemisphere,  with  high  barometer  to  the  right  and  low  barom- 
eter to  the  left  of  the  direction  in  which  they  blow,  but  that 
this  direction  inclines  a  little  toward  the  area  of  low  barometer. 
Mr.  Ley  was  the  first  to  determine  the  average  angle  of  incli- 
nation in  large  cyclones  from  a  large  number  of  observations 
made  in  the  British  Islands  and  the  adjacent  parts  of  the  con- 
tinent.39 His  results  were,  i°,  that  the  winds  commonly  incline 
from  the  districts  of  higher  toward  those  of  lower  pressure  ;  2°, 
that  this  inclination  is  much  greater  at  inland  than  at  well 
exposed  sea-stations.  The  collective  mean  result  for  15  sta- 
tions was  an  angle  of  inclination  of  20°  31'.  The  mean  for  five 
of  the  well  exposed  sea-stations  was  12°  49',  while  for  five  of 
the  most  inland  stations  it  was  28°  53'.  This  is  in  accordance 
with  the  theory,  by  which  the  angle  is  increased  by  increase  of 
friction  at  the  earth's  surface.  He  also  obtained  a  much  larger 
inclination  on  the  east  than  on  the  west  side  of  the  cyclones. 

Subsequently  Mr.  Ley  determined  the  relation  between  the 
direction  of  both  the  under  and  upper  currents  of  the  air  in 
areas  of  low  pressure  from  a  much  larger  number  of  observations 
in  the  British  Islands,  France,  Spain,  Switzerland,  Austria, 
Turkey,  Russia,  Denmark,  Sweden  and  Norway.40 

His  table  of  results  is  so  important,  not  only  for  our  present 
purpose,  for  which  only  those  results  belonging  to  the  surface 
are  needed,  but  likewise  in  comparisons  further  on  (§  205),  that 
we  shall  give  it  here  in  full,  though  in  a  different  form  and  dif- 
ferent notation.  The  following  table  and  accompanying  figure, 
taken  from  the  Meteorological  Researches,  Part  II,  Coast  Sur- 
vey Report  for  1878,  give  his  numerical  results.  Each  area 
of  low  pressure  was  divided  into  16  districts  as  represented  in 
Fig-  3-  Considering  for  the  present  the  results  only  of  the  sur- 
face winds,  we  find  that  the  average  angle  with  the  radius  for 
the  exterior  districts,  denoted  by  the  large  letters,  is  64°. 6,  and 
for  the  interior  districts,  denoted  by  the  smaller  letters,  65°. 9. 


264 


CYCLONES. 


SURFACE  WINDS. 

UPPER  CURRENTS. 

Districts. 

No.  of  observations. 

Mean  angle  with 
radius. 

No.  of  observations. 

Mean  angle  with 
radius. 

A 

198 

62° 

51 

—5° 

B 

407 

52 

173 

163 

C 

5" 

48 

226 

152 

D 

675 

54 

290 

146 

E 

803 

66 

328 

124 

F 

378 

76 

199 

IOI 

G 

277 

79 

81 

96 

1         H 

196 

80 

43 

99 

a 

195 

65 

58 

172 

!         b 

39i          f 

53 

104 

130 

c 

426 

58 

94 

135 

d 

454 

55 

141 

1  02 

e 

629 

64 

135 

73 

f 

402 

74 

142 

5i 

g 

250 

77 

83 

90 

h 

204 

81 

46 

1  06 

This  gives  an  average  inclination  of  about  25°,  a  little  greater 
than  before.     But  he  now  has  mostly  inland  stations  and  only 


Fig.  3. 

few  coast  stations  in  comparison,  and  so  this  is  also  a  confirma- 
tion of  theory. 

From  the  Weather  Maps  ofthe  United  States  Signal  Service 
for  the  years  1872  and  1873  Professor  Loomis  obtained  an  aver- 
age inclination  of  nearly  47°,  which  is  much  greater  than  that 
obtained  by  Mr.  Ley  for  Europe.  These  two  results,  however, 
are  not  inconsistent  with  each  other.  The  difference  may  be 
in  a  small  measure  due  to  difference  of  latitude,  since  theory 


COMPARISONS    WITH  OBSERVATIONS.  26$ 

Tequires  greater  inclinations  for  lower  than  for  higher  latitudes, 
but  it  is  no  doubt  due  mostly  to  the  fact  that  Loomis  took  in 
all  observations  within  isobars  of  29.9  inches,  and  hence  many 
cases  of  only  very  small  velocities,  while  Mr.  Ley  took  in  cases 
mostly  of  the  more  violent  winds  nearer  the  centres  of  the  cy- 
clones. The  winds  from  the  outer  border  of  the  cyclone  proper, 
where  the  motion  of  the  air  is  more  toward  the  centre  and  has 
not  yet  assumed  much  gyratory  velocity,  of  course,  have  a 
greater  inclination  than  those  nearer  the  centre,  where  the  gy- 
ratory velocity  is  greatest,  and  where,  it  has  been  shown,  the 
inclination  must  be  less  (§  175). 

In  subsequent  researches  with  a  greater  number  of  observa- 
tions and  measurements  taken  from  the  Signal  Service  Weather 
Maps,  Loomis41  deduced  an  average  inclination  a  few  degrees 
less  than  that  given  above.  From  this  discussion  it  resulted 
that  the  inclinations  at  smaller  distances  from  the  centre  are 
less  than  at  greater  distances.  This  is,  again,  in  accordance 
with  theory.  The  inclinations  ranged  from  about  37°  for  an 
average  distance  of  250  kilometers  to  44°  at  the  average  dis- 
tance of  1,200  kilometers. 

The  average  inclination  which  he  obtained  at  the  same  time 
for  low  barometric  pressures  from  Hoffmeyer's  charts  of  the 
northern  part  of  the  North  Atlantic  ocean  is  considerably  less 
than  in  the  preceding  case,  as  it  should  be  in  the  case  of  a  water 
surface,  where  the  friction  is  less.  The  inclination  in  this  case 
likewise  increased  with  increase  of  distance  from  the  centre, 
being  2^.4.  at  the  distance  of  278  kilometers,  and  34°.8  at  the 
distance  of  1535  kilometers.  For  barometric  pressures  above 
760  mm.  the  inclinations  were  still  larger. 

The  late  J.  Allen  Brown  from  the  observations  of  Makers- 
town,  Dublin  and  Greenwich,  1843-1848,  obtained  the  following 
results: — 54 

Jan.  Feb.  Mar.  April  May  June  July  Aug.  Sept.  Oct.  Nov.  Dec.  Year 
6    =  257°  293  267   260   22  262  274  287  284  267  240  255  269 
•0   =  247  280  239   260    o  240  249  264   243  245  226  257  249 

6—0  =   20    13    28      O    22    22    25    23     41    22    14   —2    2O 

in  which,  reckoned  from  N.  around  by  E  , 

6  =  the  direction  of  the  isobars. 
<p  =  the  direction  of  the  wind. 


266  CYCLONES. 

The  deviation,  therefore,  of  the  direction  of  the  wind  from  that 
of  the  isobar  is  20°  to  the  left  on  the  average  of  the  year. 

The  following  contains  the  average  directions  of  the  cirri, 
^  (day  only),  and  the  average  directions  of  the  surface  winds 
0,  made  day  and  night: 

Jan.  Feb.  Mar.  April  May  June  July  Aug.  Sept.  Oct.   Nov.  Dec.  Year 
iff        =  279°   303      301      242     291     263    269    267     274    276     236     308     277 

<p     =241   287   244    274    24   233  230  247   244  237   211   249   243 

ip—(f>=  38   16   57  —32  —94   30   39   20   30   39   25   59   34 

These  results  indicate  that  for  the  average  of  the  year  the- 
upper  currents  come  from  a  direction  34°  to  the  right  of  the 
surface  winds,  and  that  they  come  from  the  right  in  the  case  of 
each  separate  month  except  two.  Supposing  the  winds  to  be. 
mostly  cyclonic,  this  confirms  the  theoretical  deduction  of  §  178. 

Mr.  Brown  also  stated  that  M.  Quetelet  observed  the  direc- 
tions of  the  cloud  motions  (without  distinction  of  species)  at  the 
Brussels  observatory  during  the  years  1833  to  1846,  and  found 
the  resultant  direction  by  Lambert's  formula  to  be  for  the  14. 
years  tp  =  257°  50'.  Also  that  by  noting  the  difference  of  di- 
rections of  surface  currents  and  different  kinds  of  clouds,  he  ob- 
tained from  the  averages  of  large  numbers  of  observations, 

Cirrus  current  — Surface  currents,  orif)—0=2g°.6 

Cirro-stratus  current —      "  =22  .8 

Cumulus  current       —  =14  .5 

This  is  likewise  a  confirmation  of  the  deduction  that  high  cur- 
rents come  from  a  direction  to  the  right  of  the  lower  currents 
and  the  higher  the  more  so. 

The  observations  of  Padre  Viftes42  on  the  hurricanes  of  the 
Antilles  also  show  that  there  is  an  inclination  of  the  winds  to- 
ward the  centre,  and  that  this  is  least  nearest  the  centre.  In  all 
these  hurricanes  it  was  observed  that  "  the  gyrating  winds  cease 
to  be  circular  at  a  long  distance  from  the  vortex,  and  are  found 
to  deviate  from  the  tangent  to  the  circle  with  an  inclination  to- 
ward the  centre,  forming  a  kind  of  large  converging  spiral." 
This  converging  is  likewise  said  to  "  vary,  not  only  in  different 
hurricanes,  but  likewise  in  the  same  hurricane  with  different  di- 
rections and  intensities  of  the  wind,  and  with  different  distances. 


COMPARISONS    WITH  OBSERVATIONS.  26? 

from  the  vortex."  In  the  same  connection  it  is  also  stated  that 
it  is  "  especially  small  at  no  great  distance  from  the  vortex." 

In  more  recent  researches  Hilderbrandsson43  has  deduced 
from  observations  at  Upsala,  including  those  for  both  high  and 
low  pressures,  an  average  inclination  of  40°. 2,  and  for  the  aver- 
age of  the  three  maritime  stations  Waderobed,  Utklippau,  and 
Landou,  32°. 2.  He  likewise  obtained  for  these  three  stations,, 
as  Ley  did  for  the  British  Isles,39  Hoffmeyer  in  Denmark,44 
and  Spindler  in  Russia,45  a  larger  angle  of  inclination  on  the- 
east  than  on  the  west  side  of  the  cyclone.  This  angle  also  in- 
creased with  increase  of  distance  from  the  centre,  though  the 
differences  near  the  centre  were  very  small. 

The  following  is  the  summary  of  the  practical  results  ob- 
tained by  Captain  Toynbee  from  a  discussion  of  the  observa- 
tions of  the  North  Atlantic  Ocean  during  the  great  cyclone  of 
the  24th  and  2$th  of  August,  1873 : 

1.  There  is  strong  evidence  that  the  wind  in  a  hurricane 
draws  in  towards  its  centre. 

2.  The  indraught  is  probably  greater  in  one  quarter  than 
another. 

3.  The  indraught  is  probably  greater  near  the  centre  than- 
farther  from  it. 

The  average  inclination  from  all  the  observations  was  29°, 
the  average  latitude  being  about  the  parallel  of  50°. 

Piddington  gives  as  an  effect,  and  also  a  proof,  of  the  in- 
clination of  the  winds  toward  the  centre,  that  ships  are  often 
surrounded  or  have  their  decks  covered,  during  the  passage  of 
the  calm  centre  of  cyclones  in  the  neighborhood  of  land,  with 
land  and  aquatic  birds,  butterflies,  horseflies,  etc.  He  says : 

"  They  must  be  carried  inwards  by  the  incurving  of  the  winds,  and  at 
the  centre  are  kept  there  because  they  cannot  fly  out  of  it,  and  when  the 
ship  reaches  it  of  course  they  make  a  last  effort  to  reach  her  as  a  resting, 
place." 

181.  From  the  deductions  of  theory  confirmed  and  supple- 
mented by  numerous  observations,  it  is  evident  that  many  of 
the  usual  rules  and  sailing  directions  must  be  very  much  modi- 


:268  CYCLONES. 

fied,  especially  in  low  latitudes.  Although  the  horn-cards  of 
Piddington,  and  all  rules  based  upon  the  strictly  circular  the- 
ory of  the  winds,  may  be  still  used  at  sea  in  high  latitudes 
without  great  error,  yet  nearer  the  equator  they  must  become 
more  erroneous,  and  almost  entirely  fail  very  near  the  equator. 
It  is  beginning  to  be  pretty  generally  acknowledged  that  in 
sailing  directions  in  a  storm,  some  allowance  should  be  made 
for  a  certain  small  amount  of  inclining  of  the  winds  toward  the 
•centre,  but  it  seems  to  be  thought  that  this  should  be  the  same 
.at  all  latitudes  and  at  all  distances  from  the  centre  of  the 
storm.  If  in  low  latitudes  the  inclination  of  the  winds  accord- 
ing to  theory  may  be  60°  or  more,  the  usual  rules  for  the  deter- 
mination of  the  direction  of  the  dangerous  centre  of  the  storm 
based  upon  the  circular  theory  would  lead  to  an  error  of  five 
or  six  points  of  the  compass.  Not  only  latitude,  but  distance 
from  the  centre  also,  should  be  taken  into  account.  While 
the  centre  of  a  cyclone  is  yet  at  a  considerable  distance  and 
the  winds  have  not  yet  a  great  gyratory  velocity,  they  may, 
•even  in  high  latitudes,  have  a  considerable  inclination  toward 
the  centre,  and  nearer  the  equator  they  may  be  nearly  radial; 
but  even  in  these  latitudes,  at  places  near  the  centre,  where 
the  velocities  are  very  great,  the  gyrations  may  become  nearly 
•circular. 

The  preceding  is  confirmed  by  rules  recently  laid  down  by 
Dr.  Doberck  from  observations  made  in  the  China  Sea  and  in 
the  Philippine  Islands.  He  says:49 

"  The  whereabouts  of  the  centre  of  a  typhoon  may,  in  the  China  Sea, 
be  ascertained  by  the  rule :  Stand  with  your  back  to  the  wind,  and  you 
will  have  the  centre  on  your  left  side,  but  between  2  and  4  points 
in  front  of  your  left  hand.  There  are,  however,  certain  exceptions  to 
this  rule.  Thus  there  often  blows  a  steady  easterly  gale  along  the 
southern  coast  of  China  when  a  typhoon  is  crossing  the  China  Sea,  and 
the  gale  blows  often  steady  from  northeast  about  the  northern  entrance 
to  the  Formosa  Straits  when  there  is  a  typhoon  in  a  more  southern  lati- 
tude." 

Again  he  says :  " 

"  Further  researches  have  shown  that  in  the  Philippine  Islands  and 
.-along  the  Coast  of  China  as  far  north  as  24°  latitude,  when  you  stand 


COMPARISONS    WITH  OBSERVATIONS.  269 

with  your  back  to  the  wind  in  a  typhoon,  you  will  probably  have  the 
centre  nearly  4  points  in  front  of  your  left  hand  ;  but  on  the  open  sea  far 
from  any  shore  you  will  generally  have  it  about  3  points  in  front  of  your 
left  hand  when  your  ship  is  in  front  of  the  centre  of  the  typhoon,  and 
more  than  3  points  in  front  of  your  left  hand  behind  the  centre.  Above 
25°  latitude  the  angle  will  probably  be  found  to  be  between  2  and  3 
points.  It  appears  to  be  smaller  the  greater  the  distance  from  the  near- 
est shore  and  the  greater  the  latitude.  At  some  distance  behind  the 
centre  the  wind  blows  generally  straight  towards  it. 

182.  With  regard  to  the  ring  of  high  pressure  with  its  max- 
imum corresponding  to  the  heavy  circle  in  Fig.  I,  there  are 
many  observations  which  indicate  that  it  really  exists,  and  is; 
sensible  to  observation  in  all  well-developed  cyclones.  This 
is  not  shown  so  clearly  from  observations  made  at  the  same 
time  over  different  parts  of  the  cyclonic  area,  and  presented  in 
synoptic  charts,  as  from  observations  made  at  different  times 
at  the  same  place  while  the  whole  system  of  motions  and 
pressures  pass  over ;  though  in  the  former  case  it  is  generally 
observed  that  around  an  area  of  low  pressure  the  barometer 
stands  a  little  higher  than  the  general  average.  Before  all 
great  storms  it  is  frequently  observed  that  the  barometer- 
stands  unusually  high,  and  the  same  soon  after  it  has  passed. 
This  was  first  noticed  and  remarked  upon  by  Redfield.  These 
are  the  times  when  the  ring  of  high  pressure  around  the  cy- 
clone in  its  progressive  motion  passes  over  the  place  of  obser- 
vation. At  Havana,  Cuba,  over  which  the  tropical  cyclones  of 
great  violence  frequently  pass,  the  zone  of  high  pressure  is  dis- 
tinctly observed,  both  before  and  after  the  passage  of  the  cen- 
tral part  of  low  pressure  and  great  violence  ;  and  the  abnor- 
mally high  pressure  which  precedes  is  usually  regarded  as  an 
indication  of  the  approach  of  a  cyclone.  The  approach  of  the 
hurricane  of  September,  1875,  was  indicated  at  Havana  by  a 
sudden  rise  of  the  barometer  while  the  cyclone  was  yet  at  the 
Windward  Islands,  about  1200  miles  distant.48  Also,  on  the 
1 3th  of  September,  1876,  there  was  a  great  rise  of  the  barome- 
ter at  Havana  while  a  cyclone  was  causing  great  destruction 
on  the  Island  of  Porto  Rico.42 

Espy  remarks,  in  his  Fourth   Meteorological  Report,  that 


-2/0       „;,  CYCLONES. 

41  A  sudden  rise  of  the  barometer,  especially  in  low  latitudes,  is 
a  proof  that  there  is  a  storm  in  the  neighborhood,  and  is  one 
of  the  first  indications  of  an  approaching  storm."  On  the  1st 
of  September,  1845,  at  Fort  Brooke,  Florida,  at  the  very  time 
there  was  a  most  violent  hurricane  approaching,  and  was 
within  4°  or  5°  of  the  place,  the  barometer  arose  there  that 
morning  0.15  in.,  though  it  had  been  nearly  stationary  for 
more  than  a  month  before.  A  great  storm  of  rain  reached 
there  that  day ;  and  then  in  the  afternoon  the  barometer  fell 
0.3  in.  Espy  considered  it  a  fact  fully  established  that  without 
.such  a  rise  no  storm  of  dangerous  violence  need  be  feared,  but 
that  the  converse  of  it  was  not  true.  The  barometer  rises  where 
the  violent  part  of  the  storm  passes  by  one  side  or  the  other. 

We  also  have  evidence  of  this  ring  of  high  barometer  from 
^observations  in  the  southern  hemisphere.  The  gale  observed 
at  Kerguelen  by  the  exploring  party  of  the  Challenger  "  were 
preceded  by  an  unusually  high  barometer,  which  fell  rapidly  as 
the  storm  began  from  the  north  ;  as  the  wind  shifted  to  the 
west  the  barometer  rose." 

183.  The  observations  of  the  upper  currents  of  the  air  are 
-more  vague  and  uncertain.  But  even  here  the  results  of  the 
•observations  confirm  the  motions  given  in  the  preceding  figure 
for  the  upper  strata  of  the  atmosphere.  From  620  observa- 
tions of  the  motions  of  cirrus  clouds,  Mr.  Ley46  arrived  at  the 
following  general  law  showing  the  relation  between  the  direc- 
tion of  the  higher  currents  of  the  atmosphere  and  the  distribu- 
tion of  pressure  at  the  earth's  surface  :  The  higher  currents  of 
•the  atmosphere,  while  moving  commonly  with  the  highest  pressures, 
in  a  general  way,  on  the  right  of  their  course,  yet  manifest  a  dis- 
tinct centrifugal  tendency  over  the  areas  of  low  pressure,  and  a 
centripetal  over  those  of  high. 

This  "  centrifugal  tendency  over  the  areas  of  low  pressure" 
is  represented  by  the  dotted  arrows  within  the  dotted  circle  of 
Fig.  I,  these  observations  having  been  made  on  the  motions  of 
•cirrus  clouds  which  are  always  at  high  altitudes,  where  the 
radial  component  of  motion  is  outward,  but  yet  generally  not 
so  high  that  the  gyrations  are  anti-cyclonic. 


COMPARISONS    WITH  OBSERVATIONS. 

This  keen  observer  of  air  currents  and  cloud  motions,  and 
•generally  riot  seeking  a  confirmation  of  any  theoretical  law, 
has  likewise  observed  air  currents  which  corroborate  in  a  re- 
markable manner  the  counter-motions  of  the  air  at  the  earth's 
surface  and  at  high  altitudes,  as  delineated  in  Fig.  I  between 
-the  heavy  solid  and  dotted  circles.  He  says : 

"  There  occur  at  rare  intervals  in  Western  Europe  depression  systems, 
which  affect,  but  in  a  very  singular  way,  the  directions  of  the  upper-cur- 
:rents,  reversing  them  so  that  they  become,  on  all  sides  of  the  area, 
nearly  or  quite  in  opposition  to  Ballot's  law ;  that  is  to  say,  there  exists 
-a  direct  (anti-cyclonic)  upper  current  circulation  above  a  retrograde 
(cyclonic)  circulation  of  the  surface  winds." 

It  is  seen  from  the  figure  that  within  a  certain  belt  the  cur- 
rents below  and  above  are  reversed.  But  this  is  only  when 
the  upper  currents  are  at  very  high  altitudes,  above  the  average 
height  of  the  cirrus  clouds.  This  reversion  of  the  currents  is 
therefore  said  to  occur  at  only  rare  intervals ;  that  is,  when  the 
•cirrus  clouds  observed  are  unusually  high. 

The  following  figure,  given  by  Hildebrandsson,  represents 


.  Jfin. 

Fig.  4. 

the  results  of  his  observations  of  the  cirrus  clouds  at  Upsala 
on  the  average  for  the  year.  The  left-hand  figure  represents 
the  observations  for  barometric  pressures  less  than  760  mm. 
and  corresponds  with  the  interior  part  of  Fig.  I.  The  exterior 
part,  those  of  barometric  pressures  greater  than  760  mm.,  and 
corresponds  with  the  exterior  part  of  Fig.  I  beyond  the  isobar 
of  760  mm.  It  is  seen  that  the  arrows  incline  out  from  low 
toward  high  barometer,  as  in  Fig.  I  ;  but  in  no  case  do  they 


2/2  CYCLONES. 

indicate  completely  anti-cyclonic  gyrations,  as  in  Mr.  Ley's  rare 
cases,  the  average  altitude  of  the  observations  not  being  great 
enough  for  that. 

From  an  examination  of  121  cases  of  high  winds  on  Mount 
Washington,  by  classifying  them  with  reference  to  the  direc- 
tion of  lowest  pressure,  Professor  Loomis  deduced  the  follow- 
ing conclusions : 

"  i.  High  winds  on  Mount  Washington  circulate  about  a  low  centre 
as  they  do  near  the  level  of  the  sea.  2.  The  motion  of  the  winds  is 
nearly  at  right  angles  to  the  direction  of  low  centre.  3.  The  low  centre 
at  the  height  of  Mount  Washington  lies  behind  the  low  centre  at  the  sur- 
face of  the  earth  as  much  as  200  miles." 

At  the  height  only  of  Mount  Washington  we  would  expect 
to  find  the  winds  blowing  with  reference  to  the  centre  of  the 
cyclone  very  nearly  as  at  sea-level,  since  it  is  far  below  the 
neutral  plane  where  the  radial  component  of  motion  is  out- 
ward from  the  centre,  and  especially  lower  than  the  altitude  at 
which  the  gyrations  become  anti-cyclonic.  But  as  the  motions 
at  the  neutral  plane  become  circular  we  would  expect  them  to 
deviate  but  little  from  a  circular  motion  at  the  top  of  Mount 
Washington,  and  so  be  nearly  at  right  angles  to  the  direction 
of  the  low  centre.  The  third  deduction  of  Professor  Loomis 
is  explained  by  the  circumstance  that  the  temperature  of  the 
air  is  not  symmetrical  on  all  sides  of  the  cyclone  and  is  colder 
on  the  west  than  the  east  side  of  the  centre,  as  represented  in 
§  191,  Fig.  5.  Taking  two  points  on  each  side  in  the  line  of 
progressive  motion  of  the  centre  where  the  pressures  on  the 
earth's  surface  are  equal,  as  we  ascend  on  the  colder  side  the 
pressure  decreases  faster  than  on  the  east  side  on  account  of 
the  greater  density  of  the  air,  and  so  after  arriving  at  a  given 
altitude  the  pressure  on  the  rear  side  is  less  than  on  the  front 
side.  This  throws  the  point  of  lowest  pressure  on  the  level 
above  a  little  behind  that  on  the  earth's  surface.  On  the  latter 
the  low  centre  is  perhaps  near  the  medium  point  between  points 
of  equal  pressure ;  but  above,  it  is  near  the  medium  point  be- 
tween equal  pressures  there,  and  so  behind  the  middle  point 
or  point  of  lowest  pressure  below. 


GRADUAL  ENLARGEMENT  OF  CYCLONES.  2/3 


GRADUAL   ENLARGEMENT   OF  CYCLONES. 

184.  In  the  preceding  consideration  of  cyclones  it  has  been 
supposed  that  the  whole  system  of  circulation  has  a  definite 
limit,  and  comprises  at  all  times  the  same  air,  which,  by  means 
of  the  vertical  circulation,  is  being  continually  interchanged 
between  the  interior  and  exterior  parts  within  this  limit.  This, 
however,  is  far  from  being  the  case  in  nature.  As  long  as  the 
vertical  circulation  is  maintained  with  increasing  or  at  least 
sufficient  energy,  the  tendency  of  the  cyclone  is  to  extend 
farther  and  farther  from  the  centre,  and  so  to  continually  ex- 
tend the  gyrations  and  the  whole  system  of  circulation  over  a 
greater  area.  But  unless  the  energy  which  sustains  it  increases, 
likewise,  it  must  reach  a  limit,  for  otherwise  the  temperature 
gradient  and  the  forces  upon  which  the  vertical  circulation 
depends  become  barely  sufficient  to  overcome  the  frictional 
resistances,  when  further  enlargement  must  cease  ;  and  then, 
as  the  energy  begins  to  fail,  either  through  a  diminution  of  the 
supply  of  aqueous  vapor  or  a  change  in  the  relative  temper- 
atures of  the  lower  and  upper  strata  by  means  of  the  inter- 
change of  air  in  the  vertical  circulation,  the  whole  system  of 
circulation  must  gradually  become  wreaker  and  finally  entirely 
subside. 

It  may  be  that  cyclones  mostly  commence  over  a  small 
area  and  gradually  enlarge,  but  this  is  not  necessarily  so.  If  the 
atmosphere  is  in  an  unstable  state,  and  the  temperature  con~ 
ditions  (§  156)  are  such  that  the  initial  upward  motion  takes, 
place  over  a  large  area  at  once,  then  the  vertical  and  gyratory 
circulations  begin  at  once  over  a  large  area  and  gradually  grow 
in  strength  until  the  frictional  resistance  from  increase  of  veloc- 
ity becomes  equal  to  the  force,  when  further  increase  in  vio- 
lence, as  well  as  extent  of  limits,  must  cease.  There  is  there- 
fore a  certain  limit  to  the  extent  and  violence  of  a  'cyclone 
somewhat  proportional  to  the  amount  of  energy ;  and  if  the 
initial  temperature  conditions  are  such  as  to  start  it  over  a. 


274  CYCLONES. 

small  area  only,  it  gradually  increases  in  both  extent  and 
violence  until  this  limit  is  reached. 

As  the  area  is  gradually  enlarged  and  air  from  greater  dis- 
tances is  brought  in,  there  must  be  such  an  adjustment  between 
the  cyclonic  and  anti-cyclonic  gyrations  as  to  satisfy  the  prin- 
ciple of  §  171,  and  so  the  extent  of  both  must  increase  together, 
and  also  that  of  the  ring  of  highest  barometer. 

The  observed  dimensions  of  the  violent  part  of  cyclones 
are  very  different,  especially  in  different  latitudes.  In  the 
Indian  Ocean,  and  especially  in  the  Bay  of  Bengal,  and  also  in 
the  China  Sea,  they  are  said  to  be  comparatively  small,  rang- 
ing from  50  to  250  miles  in  diameter.  According  to  Redfield 
the  cyclones  in  the  lower  latitudes  of  the  western  part  of  the 
Atlantic  Ocean  are  of  about  the  same  dimensions. 

Piddington  says : 54 

"  In  the  West  Indies  the  researches  of  Mr.  Redfield  and  Col.  Reid 
seem  to  show  that  though  while  approaching  to,  or  within,  the  Islands 
they  are  sometimes  as  small  as  100  or  150  miles  in  diameter,  they  may, 
and  it  would  seem  most  frequently  do,  after  reaching  the  Atlantic  Ocean, 
dilate  considerably,  and  then  often  attain  to  600  or  even  1000  miles  in 
diameter,  the  wind  blowing  an  excessively  severe  gale  over  all  this  area, 
and  toward  its  centre  becoming  of  true  hurricane  violence,  and  the 
whole  vortex,  so  whirling,  travels  over  thousands  of  miles  of  track." 

He  further  says : 

"The  typhoons  (cyclones)  of  the  China  Sea  appear  to  vary  from  60 
or  80  miles  to  three  or  four  degrees  in  diameter." 

In  the  middle  and  higher  latitudes,  however,  they  are  gen- 
erally from  1000  to  1500  miles,  and  often  much  more,  in 
diameter.  As  a  rule  the  diameters  are  much  greater  in  the 
higher  than  in  the  lower  latitudes.  But  tropical  cyclones  are 
observed  at  sea  and  those  of  high  latitudes  mostly  on  land, 
and  those  observed  at  sea  have  perhaps  mostly  originated  on 
the  continents,  and  the  difference  may  lie  in  the  places  of 
origin,  those  originating  at  sea  being  generally  smaller. 


PROGRESSIVE  MOTIONS  OF  CYCLONES.  2?$ 


PROGRESSIVE   MOTIONS   OF  CYCLONES. 

185.  Ordinary  cyclones  are  never  stationary,  and  the  di- 
rections in  which  their  centres  move  and  their  velocities  vary 
not  only  in  different  latitudes  and  regions  of  the  globe,  but  in 
the  same  places  at  different  times.  In  general  their  tendency 
in  lower  latitudes  is  westerly,  and  in  the  middle  and  higher 
latitudes  easterly.  There  are  several  circumstances  which  con- 
trol, to  a  greater  or  less  extent,  the  progressive  motions  of 
cyclones.  The  principal  one  of  these  is  undoubtedly  the  gen- 
eral motion  of  the  atmosphere  in  which  they  exist,  not  at  and 
near  the  earth's  surface  merely,  but  at  high  altitudes  where  the 
centre  of  energy  is.  This  carries  them  along  as  a  stream  of  water 
carries  along  the  small  whirling  eddies  which  are  formed  in  it. 
This  idea  was  first  suggested  by  the  writer  more  than  a  quarter 
of  a  century  ago.47  Tropical  cyclones  move  westward,  or  at  least 
have  a  large  west  component,  because  the  general  motion  of 
the  atmosphere  there,  up  to  a  considerable  altitude,  is  westerly, 
while  in  the  higher  latitudes  cyclones  move  in  an  easterly 
direction  with  much  greater  velocities,  because  there  the  gen- 
eral motion  at  all  altitudes  is  easterly,  and  the  velocity,  espe- 
cially at  high  altitudes,  is  comparatively  great.  The  average 
direction  for  the  United  States,  as  determined  by  Loomis 
from  an  examination  of  the  individual  directions  laid  down  on 
the  Weather  Maps  of  the  Signal  Service  for  three  years,  com- 
prising 485  cases,  is  N.  81°  E.,  with  an  average  velocity  of  26 
miles  per  hour.  The  monthly  averages  indicate  an  annual 
inequality.  For  April  to  September,  inclusive,  it  is  N.  82°.5  E. 
23  miles,  and  for  October  to  March,  inclusive,  N.  78°. 5  E.  29 
miles  per  hour.  Hence  the  direction  is  more  nearly  toward  the 
east  and  the  velocity  greater  in  winter  than  in  summer. 

The  rate  of  progress  of  cyclone  centres  over  the  North  At- 
lantic Ocean  and  over  Europe  seems  to  be  much  less,  and  the 
annual  inequality  proportionally  less.  As  the  results  of  later 
and  more  extended  researches  Loomis 17  gives,  in  miles  per 
hour,  the  following  monthly  rates  of  progressive  motion  of 
-cyclone  centres : 


276 


CYCLONES. 


Month. 

United  States. 

Atlantic  Ocean, 
Middle  Latitudes. 

Europe. 

33.8 

17.4 

17   A 

34.  2 

iq.  i) 

18  o 

March        .              

31    c 

IO.7 

17    Z 

27.  5 

19.4 

16  2 

25  .  5 

16.6 

I/i    7 

June          .              

24   A 

17.  K 

I--    g 

Tulv    . 

24.6 

15.8 

I  A    2 

August                                                       • 

22    6 

16  •} 

September         

24    7 

17.2 

17    ^ 

27.6 

18.7 

IQ    O 

November                                           . 

2Q    Q 

20.  o 

18  6 

December     .        .            

33   A 

18.3 

17    Q 

1  /  «y 

Year 

28.4 

18.0 

16.7 

The  values  for  the  United  States  are  the  averages  of  13 
years,  1872-1884.  Those  for  the  Atlantic  Ocean  were  obtained 
from  the  monthly  storm  tracks  published  with  the  Interna- 
tional Bulletin  for  a  period  of  four  years,  1879-1882.  Those  of 
Europe,  from  the  monthly  charts  of  storm  tracks  published  by 
the  Deutsche  Seevvarte  for  five  years,  1876-1880.  The  average 
in  the  United  States  for  the  6  winter  months  is  31.7  miles, 
while  for  the  summer  it  is  24.9  miles,  the  ratio  being  very 
nearly  as  obtained  above  from  the  three  years. 

If  the  general  motions  of  the  atmosphere  have  a  controlling 
influence  upon  the  progressive  motions  of  cyclones,  then  we 
would  expect  that  these  motions  would  not  be  only  westerly  in 
lower  latitudes  and  easterly  in  the  higher  latitudes,  but  also  if 
there  is  an  annual  inequality  in  the  one  there  must  also  be 
such  in  the  other.  According  to  the  table  of  §  98  the  easterly 
velocity  in  the  middle  latitudes  is  more  than  twice  as  great  in 
January  as  in  July;  but  the  averages  for  the  winter  half  and 
the  summer  half  of  the  year  would  be  nearly  as  29  to  23  re- 
spectively, the  same  as  the  ratio  between  the  winter  and  sum- 
mer velocities  of  the  progressive  motions  of  cyclones  given 
above.  This  velocity,  however,  is  much  greater  than  that  of 
the  easterly  motion  of  the  atmosphere  in  the  lower  strata,  even 
up  to  &  considerable  altitude.  But  the  energy  of  the  cyclone, 
as  may  be  seen  from  §  159,  is  mostly  above,  where  the  conden- 


PROGRESSIVE  MOTIONS   OF  CYCLONES.  2// 

Cation  of  the  aqueous  vapor  occurs,  and  where  the  air  temper- 
ature in  the  cyclone  differs  most  from  that  of  the  surrounding 
atmosphere  ;  and  so  the  progressive  motion  is  controlled  mostly 
by  that  of  the  general  motion  of  the  atmosphere  up  at  that 
altitude.  From  the  table  of  §  98  it  is  seen  that  at  the  altitude 
of  2.5  miles  in  the  United  States  the  east  component  of  the 
general  motion  is  about  26  miles,  the  same  as  the  easterly 
velocity  of  the  cyclones. 

In  the  tropical  latitudes,  where  by  the  table  of  §  98  the 
velocity  of  the  west  component  of  motion  of  the  atmosphere 
vanishes  at  no  great  altitude,  especially  in  the  winter  season, 
the  westerly  velocity  of  the  progressive  motion  is  comparatively 
small,  and  must  be  controlled  mostly  by  the  lower  part  of  the 
-atmosphere.  It  is  remarkable  that  this  westerly  progression 
of  tropical  cyclones  occurs  almost  exclusively  at  a  season  when 
the  westerly  velocity  of  the  atmosphere  extends  the  highest  up. 

186.  There  seems  to  be  a  general  tendency  in  cyclones 
which  originate  in  the  lower  latitudes  to  move  toward  the 
poles,  but  observations  are  wanting  to  show  that  this  is  the  case 
everwhere  without  exceptions.  Such  a  tendency  may  arise 
from  the  deflecting  force  due  to  the  earth's  rotation  being 
greater  for  equal  gyratory  velocities  on  the  polar  than  on  the 
equatorial  sides  of  cyclones,  this  force  being  as  the  sine  of  the 
latitude.  Hence  the  tendency  of  the  gyrating  air  on  the  polar 
side  to  move  toward  the  pole  is  greater  than  that  of  the  air  on 
the  equatorial  side  to  move  toward  the  equator,  and  so  the 
difference  between  these  unbalanced  counter  forces  tends  to 
draw  the  whole  system  toward  the  pole,  since  the  condensation 
of  aqueous  vapor  and  centre  of  energy  are  in  the  cyclonic  part, 
and  so  the  whole  system  of  gyration  must  follow  it.  It  is  evi- 
dent that  such  a  tendency  must,  for  cyclones  of  the  same  ex- 
tent, be  greatest  near  the  equator,  where  the  sines  of  the  lati- 
tudes on  the  two  sides  differ  most,  and  be  comparatively  small 
in  high  latitudes,  where  the  difference  between  the  sines,  even 
for  large  differences  of  latitude,  is  small. 

But  the  directions  and  velocities  of  progressive  motion  are 
also  much  influenced  by  the  irregularities  and  deflections  of 


2/8  CYCLONES. 

the  general  motions  of  the  atmosphere,  caused  by  the  conti- 
nents and  mountain  ranges,  as  explained  in  §  123  and  follow- 
ing ones.  Hence  on  the  east  coasts  of  the  United  States,  of 
China,  and  of  South  Africa,  where  mostly  tropical  cyclones 
pass  up  into  the  higher  latitudes,  they  simply  drift  in  the 
prevailing  current,  but  are  probably  somewhat  aided  by  the  in- 
fluence referred  to  above.  On  the  eastern  sides  of  the  conti- 
nents near  the  tropics,  where  the  deflections  and  the  general! 
currents  are  mostly  toward  the  equator,  as  west  of  Northwest 
Africa  and  of  Mexico,  there  is  no  well  authenticated  account 
of  cyclones  having  passed  from  lower  to  higher  latitudes.  We 
have,  however,  a  reliable  account  of  a  very  violent  and  destruc- 
tive cyclone  passing  in  a  direction  from  the  equator  toward  the 
pole  in  the  Fiji  Islands  with  a  velocity  of  about  ten  miles  per 
hour,  where  there  is  no  known  cause  for  a  general  current  of  the 
atmosphere  toward  the  pole.48  This  occurred  on  the  3d  and  4th 
of  March,  1886.  Its  track  was  traced  not  quite  to  the  parallel 
of  20°  S.,  but  here  it  seemed  to  be  inclining  around  toward  the 
east,  as  if  already  feeling  the  influence  of  the  easterly  cur- 
rents of  more  southerly  latitudes.  This  cyclone  was  a  charac- 
teristic one  of  these  latitudes,  of  small  diameter,  about  300 
miles,  minimum  pressure  of  27.63  in.,  and  of  extraordinarily 
steep  gradients,  estimated  at  one  inch  of  mercury  in  a  distance 
of  63  miles. 

187.  From  the  combined  action  of  the  two  preceding  prin- 
ciples, namely,  that  cyclones  have  a  tendency  to  move  with 
the  general  atmospheric  current  in  which  they  exist,  and  that 
they  at  the  same  time  tend  to  move  toward  the  poles,  all  cy- 
clones which  originate  near  the  equator  must  first  move  in  a 
westerly  direction  and  also  toward  the  pole,  after  arriving  at  the 
parallel  of  about  30°,  which  is  the  dividing  line  between  the 
westerly  and  easterly  motions  of  the  strata  which  mostly  con- 
trol the  progressive  motion  of  the  cyclone,  the  tendency  must 
be  toward  the  pole  only,  but  after  arriving  in  still  higher  lat- 
itudes, where  the  general  motion  of  the  atmosphere  is  easterly,. 
the  resultant  motion  must  be  northeasterly,  and  finally  after 
reaching  still  a  higher  latitude,  where  the  polar  tendency  is. 


PROGRESSIVE   MOTIONS  OF  CYCLONES.  279 

small,  it  must -be  still  more  toward  the  east,  unless  affected  by 
some  of  the  other  controlling  influences.  Hence  the  path  of 
such  a  cyclone  is  somewhat  of  the  form  of  a  parabola,  with  its 
vertex  at  or  near  the  tropical  calm-belt,  except  that  the  equa- 
torial branch  of  the  parabola  continues  more  on  the  same  par- 
allels of  latitude  than  the  polar  branch. 

Many  cyclones  of  this  sort  originate  during  the  latter  part  of 
summer  and  the  fall  in  the  North  Atlantic  Ocean,  apparently 
near  the  equatorial  limits  of  the  trade-winds,  which  at  first  are 
comparatively  small ;  but  they  seem  to  have  great  power  of 
continuance,  for  they  usually  run  through  the  whole  course  of 
their  parabolic  orbit,  gradually  expanding  as  they  go,  until, 
after  reaching  high  latitudes  in  the  northern  part  of  the  Atlan- 
tic, they  have  the  usual  dimensions  of  cyclones  of  these  lati- 
tudes. Being  carried  at  first  in  a  nearly  west  direction  by  the 
westerly  motion  of  the  atmosphere  in  the  trade-wind  zone,  un- 
til they  arrive  in  the  neighborhood  of  the  West  India  Islands 
and  the  Gulf  of  Mexico,  they  then  curve  around  toward  the 
north  over  the  United  States,  or  along  the  east  coast  and  the 
Gulf  Stream,  up  into  higher  latitudes,  aided  here  in  their  polar 
movement,  no  doubt,  by  the  deflected  current  referred  to  in  § 
123.  Here  their  progressive  motions  are  controlled  mostly  by 
the  strong  easterly  tendency  of  the  atmosphere  in  these  lati- 
tudes, and  so  their  directions  become  more  toward  the  east, 
the  same  as  those  of  cyclones  having  their  origins  in  the  higher 
latitudes. 

The  rate  of  westerly  progress  of  these  cyclones  is  compara- 
tively small  while  near  the  equator,  and  it  becomes  still  smaller 
while  they  are  curving  around  into  the  higher  latitudes ;  but 
after  arriving  into  the  middle  and  higher  latitudes,  where  their 
general  direction  is  a  little,  north  of  east,  they  have  the  usual 
velocities  of  progression  of  cyclones  generally  of  these  latitudes. 
According  to  Loomis17  the  average  direction  and  velocity  of 
forty  of  these  cyclones  while  moving  westerly  was  respectively 
26°  north  of  west  and  17.4  miles  per  hour.  In  only  two  cases 
was  the  direction  south  of  west.  Of  course  the  farther  west, 
the  more  the  directions  inclined  away  from  the  equator.  The 


280  CYCLONES. 

average  direction  of  these  storms  while  moving  eastwardly  to 
the  parallel  of  40°  was  E.  38°. 5  N.,  and  the  hourly  velocity  in 
this  part  of  their  course  was  20.5  miles.  In  the  first  part  of 
this,  however,  the  course  was  more  northerly  and  gradually 
changed  around  to  a  course  only  a  little  north  of  east. 

The  steady  current  of  the  northeast  trade-winds  is  not  fa- 
vorable to  the  origination  of  cyclones,  and  therefore  they  seem 
to  originate  at  the  northern  limit  of  the  calm-belt  only,  or  at 
least  not  so  far  within  that  the  deflecting  force  depending  upon 
the  earth's  rotation  is  too  small  to  produce  gyrations ;  for,  we 
have  seen,  this  force  becomes  very  small  near  and  vanishes  at 
the  equator.  Hence,  of  the  forty  paths  of  cyclone  centres  ex- 
amined by  Loomis,  no  part  of  any  one  of  them  was  found  within 
10°  of  the  equator.  If  the  conditions  of  a  vertical  circulation 
were  found  at  the  equator,  they  would  not  give  rise  to  any  cy- 
clone, and  there  would  be  little  violence  and  no  sensible  baro- 
metric depression  in  the  centre.  In  all  seasons  of  the  year  ex- 
cept during  the  latter  part  of  summer  and  the  fall,  the  trade- 
winds  blow  down  to  a  latitude  where  the  deflecting  force  of 
the  earth's  rotation  is  too  weak  to  give  rise  to  cyclones,  and  as 
they  cannot  originate  within  the  zone  of  these  winds,  they  can 
generally  originate  at  the  time  only  in  which  these  winds  do 
not  extend  down  very  near  the  equator. 

188.  The  east  coast  of  China,  and  the  adjacent  oceans,  in- 
cluding Japan,  is  also  traversed  by  numerous  cyclones  of  this 
sort,  originating  in  the  same  manner  and  mostly  at  the  same 
season  of  the  year.  These  likewise  curve  around  in  a  kind  of 
parabolic  path  with  its  vertex  near  the  parallel  of  30°,  until 
they  arrive  in  the  higher  latitudes  and  assume  a  direction  nearly 
east  across  the  North  Pacific  Ocean.  The  rate  of  progress  is 
probably  about  the  same  as  in  the  case  of  the  tropical  cyclones 
of  the  North  Atlantic  Ocean  and  the  United  States. 

In  the  Arabian  Sea  and  Bay  of  Bengal  there  are  similar 
small  cyclones  originating  near  the  equator,  which  first  move 
only  a  little  north  of  west,  and  then  gradually  curve  around 
toward  the  north  and  are  lost  within  the  continent.  But  these 
seem  to  be  interfered  with  by  the  great  Asiatic  monsoon,  so 


PROGRESSIVE  MOTIONS  OF  CYCLONES.  28 1 

that  they  originate  mostly  spring  and  fall  at  the  times  of  the 
changes  of  the  monsoon,  when  there  is  a  month  or  more  of 
comparatively  calm  weather.  Consequently  there  is  a  tendency 
toward  two  maxima  in  the  monthly  numbers  of  cyclone  fre- 
quency, as  is  seen  in  the  following  table.  The  average  wester- 
ly velocity  of  these  cyclones,  as  obtained  by  Loomis17,  is  only 
8.5  miles  per  hour. 

On  the  eastern  coast  of  Africa  and  the  adjacent  ocean, 
including  Madagascar,  cyclones  originating  in  the  Indian  Ocean 
near  the  southern  limit  of  the  equatorial  calm-belt,  when 
it  has  its  most  southern  position  in  midwinter  of  the  northern 
hemisphere,  being  then  forced  down  to  the  parallel  of  about  12° 
S.  (§  142),  pass  around  into  middle  latitudes  of  the  southern 
hemisphere,  where  their  directions  become  more  nearly  east, 
being  controlled  there  by  the  strong  general  easterly  currents 
of  the  atmosphere  in  these  latitudes.  The  forms  of  their  paths 
are  very  similar  to  those  of  the  North  Atlantic  and  North  Pa- 
cific Oceans,  but  their  motions  in  them  are  comparatively  very 
slow,  usually  only  3  or  4  miles  per  hour.  These  being  in  the 
opposite  hemisphere,  the  time  most  favorable  for  their  origina- 
tion, and  consequently  the  time  of  greatest  frequency,  is  in 
February  intead  of  August. 

The  relative  frequency  of  the  occurrence  of  all  the  tropical 
cyclones  in  the  several  months  of  the  year  may  be  seen  in  the 
table  on  page  282. 

In  the  South  Atlantic  Ocean  the  southeast  trade-winds 
often  extend  considerably  beyond  the  equator,  and  at  any  sea- 
son too  near  the  equator  for  cyclones  of  this  class  to  originate. 
Hence  on  the  east  side  of  South  America  and  on  the  adjacent 
ocean  there  do  not  seem  to  be  any  cyclones  which  move  around 
in  a  parabolic  orbit  into  the  higher  latitudes  of  the  southern 
hemisphere. 

1 89.  Although  cyclones  are  carried  along  by  the  general 
drift  of  the  atmosphere,  yet  as  the  velocity  of  this  is  very  dif- 
ferent at  different  altitudes,  varying  circumstances  of  the 
cyclone  may  cause  great  variations  in  the  progressive  velocity, 
while  that  of  the  general  drift  remains  the  same.  According 


282  CYCLONES. 

THE  YEARLY  PERIODS  OF  CYCLONE  FREQUENCY  IN  SEVERAL  SEAS.49 


Arabian  Sea. 

Bay  of  Ben- 
gal. 

S.  Indian 
Ocean. 

Java  Sea. 

China  Sea. 

Havana. 

No.  of  years. 
No.  of  cyclones. 

Authority. 

234 
70 

Chambers. 

i39 
"5 

Blanfond. 

40 
53 

Piddington, 
Thorn  and 
Reid. 

12 

Piddington 
and  Thorn. 

85 
214 

Schuck. 

363 
355 

Poey. 

Tan.., 

6 

2 

17 

2C 

2 

j 

Feb 

o 

2C 

42 

o 

2 

Mar  

2 

IQ 

8 

2 

April  

iq 

8 

je 

8 

2 

May.. 

18 

16 

7 

o 

e 

I 

June     .  . 

20 

o 

o 

5" 

July   . 

-i 

o 

o 

IO 

12 

\  y  

•7 

4" 

o 

o 

IQ 

27 

Sept  .    . 

2 

o 

27 

2-3 

Oct     

6 

27 

2 

o 

16 

1  7 

Nov  

14. 

16 

7 

o 

8 

5' 

Dec 

8 

6 

17 

2 

as  the  central  controlling  power  of  the  cyclone  is  at  greater  or 
less  altitudes  must  the  progressive  velocity  be  greater  or  less,, 
so  far  as  it  depends  upon  the  mere  drift  of  atmosphere ;  and 
these  variations  depend  very  much  upon  the  hygrometric  state,, 
as  well  as  the  unstability,  of  the  atmosphere,  as  may  be  seen 
from  the  table  of  §  159.  Taking  the  first  example  in  which 
the  vertical  temperature  gradient  is  represented  by  the  column 
A,  it  is  seen  by  comparing  the  column  C  in  the  case  of  sat- 
uration with  that  of  A,  and  then  that  of  C '  in  the  case  of  r  —  d 
=  4°,  that  the  weight  of  the  differences,  and  consequently  the 
power  of  the  cyclone,  is  much  lower  in  the  former  case  than  in 
the  latter.  The  more  nearly,  therefore,  the  air  is  saturated, 
other  circumstances  remaining  the  same,  the  lower  down  is  the 
controlling  power,  and  consequently  the  less  must  be  the  pro- 
gressive easterly  velocity  of  cyclones  in  the  middle  latitudes. 

The  annual  inequalities  in  the  velocities  of  the  progressive 
motions  of  cyclones,  we  have  seen,  is  less  than  that  of  the 
general  easterly  velocities  of  the  wind  ;  and  this  may  be  caused 
by  the  atmosphere's  being  more  nearly  saturated  in  winter 
than  in  summer.  It  may  also  be  the  cause  of  the  greater 
velocity  of  progressive  motion  over  the  United  States  at  ali; 


PROGRESSIVE  MOTIONS  OF  CYCLONES.  28$ 

seasons  than  over  the  Atlantic  Ocean  and  Europe,  since  the 
climate  of  the  United  States  is  continental,  and  consequently 
drier,  than  that  of  the  Atlantic  Ocean  and  of  Europe,  which, 
for  reasons  given  in  §  122,  has  somewhat  of  an  oceanic  climate. 
Over  the  United  States,  therefore,  the  vapor  has  to  ascend  a 
little  higher  generally  before  condensation  takes  place,  and  so 
the  seat  of  controlling  energy  is  higher,  and  the  progressive 
velocities  of  cyclones  greater,  than  on  the  Atlantic  Ocean  and 
in  Europe. 

But  the  more  unstable  the  state  of  the  atmosphere  is,  the 
higher  is  the  central  controlling  power,  as  may  be  seen  from 
the  same  table  of  §  1 59 ;  and  so  the  rate  of  progression  also  de- 
pends upon  this  circumstance,  and  consequently  it  causes  vari- 
ations at  different  seasons  and  places. 

190.  As  the  energy  of  the  cyclone  is  mostly  in  the  aqueous 
vapor  condensed,  and  without  this  we  rarely  have  the  condi- 
tions of  more  than  an  initial  cyclonic  action,  the  velocity  and  di- 
rection of  the  progressive  motion  of  a  cyclone  depends,  to  some 
extent  at  least,  upon  the  distribution  of  this  vapor  in  the  region 
in  which  the  cyclone  exists  :  for  the  cyclone  is  likely  to  be 
drawn  somewhat  in  the  direction  in  which  there  is  the  most 
vapor,  and  to  pass  around  those  regions  in  which  there  is  little 
vapor.  It  is  for  this  reason,  perhaps,  that  the  chain  of  lakes 
between  Canada  and  the  United  States  seems  to  be  a  great 
highway  for  cyclones.  It  is  also  very  often  observed  that  cy- 
clones in  the  interior  of  the  United  States,  especially  in  winter, 
instead  of  pursuing  their  usual  easterly  direction,  strike  directly 
across  in  a  southeasterly  direction  to  the  Atlantic  coast  where 
the  air  is  warmer  and  the  aqueous  vapor  more  abundant,  beingf 
drawn  in  the  direction  from  which  they  receive  the  most  sus- 
tenance, and  then  proceed  along  the  coast  toward  Newfound- 
land. In  the  winter  season,  also,  cyclones  which  make  their 
first  appearance  on  the  Pacific  coast  of  the  United  States,  if 
not  too  far  north,  instead  of  passing  through  the  cold  and  dry 
interior  of  the  continent,  follow  the  coast  down  into  Lower 
California  and  Mexico,  and,  crossing  over  into  Texas  and  the 
gulf  region,  then  make  their  way  up  along  the  eastern  coast  of 


-284  CYCLONES. 

the  United  States,  as  is  usual  with  all  tropical  cyclones  of  that 
region  coming  from  the  direction  of  the  West  India  Islands, 
thus  seeming  to  skirt  entirely  around  the  interior  of  the  con- 
tinent on  the  warmer  and  moister  side  of  the  continent,  be- 
cause here  more  aqueous  vapor  is  found  for  their  support. 

We  have  seen  that  there  are  two  dry  belts  extending  en- 
tirely around  the  globe  (§  120),  except  so  far  as  they  are  broken 
up  by  monsoons  and  the  deflected  atmospheric  currents  of 
continents  and  mountain  ranges  (§§  124,  125).  It  is  doubtful 
whether  the  polar  tendency  of  tropical  cyclones  is  in  general 
strong  enough  to  carry  them  through  the  trade-wind  zones 
against  the  trade-winds,  and  whether  the  amount  of  vapor  in 
the  dry  belts  is  sufficient  to  sustain  them  in  their  passage  through 
them  into  higher  latitudes,  except  on  the  eastern  sides  of  the 
continents,  where  the  deflected  atmospheric  currents  counter- 
act and  change  the  directions  of  the  trade  winds  and  carry 
aqueous  vapor  with  them  for  the  support  of  the  cyclone. 
Hence  the  regions  of  these  deflected  currents  on  the  east  sides 
of  the  United  States  and  China,  and  of  the  southern  part  of 
Africa,  seem  to  be  gaps  in  the  dry  belts  through  which  alone, 
or  at  least  for  the  most  part,  tropical  cyclones  are  able  to  pass 
into  the  higher  latitudes.  We  have  had  one  notable  example, 
however  (§  186),  in  which  such  a  passage  seems  to  have  been 
made,  but  this  was  a  cyclone  of  unusual  power  and  violence ; 
and  the  passage  was  through  a  region  where  there  are  nu- 
merous and  very  large  islands. 

191.  In  all  which  precedes  upon  this  subject,  as  well  as 
upon  the  subject  of  cyclones  in  general,  no  account  has  been 
taken  of  the  effect  of  differences  of  temperature  of  the  atmos- 
phere upon  the  polar  and  equatorial  sides  of  the  cyclone,  but 
the  whole  region  of  atmosphere  in  which  the  cyclone  exists  is 
supposed  to  be  of  uniform  temperature,  except  within  the  cy- 
clonic region.  But  in  the  real  cases  of  nature,  especially  in  the 
middle  latitudes  and  in  the  winter  season,  there  is  a  great  dif- 
ference of  temperature,  where  the  cyclone  is  large,  between 
the  polar  and  equatorial  sides,  which  has  nothing  to  do  with 
the  temperature  disturbance  upon  which  the  origination  of  the 


PROGRESSIVE  MOTIONS  OF  CYCLOXES. 


285 


cyclone  depends,  but  which  give  rise  to  large  modifying  influ- 
ences after  the  cyclone  has  originated,  which  would  not  take 
place  in  an  atmosphere  of  uniform  temperature  on  all  sides 
around  the  cyclone. 

The  following  figure  represents  the  action  of  a  large  cyclone, 
say  1000  miles  in  diameter,  in  the  middle  latitudes,  in  winter, 
at  which  time  the  difference  of  temperature  on  the  two  sides 
may  be  as  much  as  20°  C.  On  the  southeasterly  and  easterly 
sides  the  cyclonic  currents,  as  represented  by  the  arrows,  carry 
the  warmer  and  moister  air  of  lower  latitudes  to  higher  ones,. 


Fig.  5. 

and  on  the  northwesterly  and  westerly  sides,  the  colder  and' 
drier  air  of  higher  into  lower  latitudes.  The  difference  of 
temperatures  between  the  west  and  east  sides  of  the  cyclones 
is  also  increased  by  terrestrial  radiation  through  the  clear  air 
on  the  west  side,  which  is  the  clearing-up  side  of  the  cyclone, 
while  on  the  other,  clouds  prevail  which  hinder  this  radiation. 
The  effect  from  both  causes  upon  the  isotherms,  which  we 
may  at  first  suppose  to  have  extended  nearly  in  an  east  and 
west  direction,  is  somewhat  as  shown  by  the  figure.  The  tem- 
perature gradient  now  is  in  the  direction  of  the  line  a  b  instead 
of  from  the  pole  toward  the  equator,  and  is  steeper,  the 
isotherms  being  closer.  Comparing  now  the  temperatures  on 
the  same  latitudes  in  the  lines  c  d  and  e  f,  as  indicated  by  the 
disturbed  isotherms,  it  is  seen  there  is  a  great  difference  and 


'286  CYCLONES. 

;a  steep  temperature  gradient  in  an  east  and  west  direction, 
where,  before  cyclonic  disturbance,  there  was  none.  Not  only 
does  the  cold  and  dry  air  on  the  west  side  tend  to  press  the 
warmer  and  moister  air  on  the  east  side  still  farther  toward  the 
east,  but  the  latter  is  continually  forming  a  new  centre  of  tem- 
perature disturbance  a  little  in  advance,  which  becomes  a  new 
•cyclone  centre,  and  so  there  is  an  apparent  progressive  motion 
from  the  tendency  to  continually  form  a  new  cyclone  a  little  in 
.advance  of  the  old  one.  Such  an  effect  would  evidently  take 
•place  in  an  atmosphere  without  any  drifting  progressive  mo- 
tion ;  but  this  effect  must  be  subordinate  to,  and  much  less 
than,  that  of  the  progressive  motion  of  the  atmosphere  ;  for,  if 
it  were  not,  since  its  action  is  always  in  a  direction  from  west 
to  east,  cyclones  in  the  tropical  latitudes  would  never  move 
westwardly. 

The  effect  of  a  cyclone  upon  the  isotherms,  as  represented  in 
the  preceding  figure,  may  be  seen  almost  any  time  upon  the 
synoptic  weather  charts  of  the  Signal  Service,  in  cases  of  well- 
•developed  cyclones ;  but  of  course  the  observed  effects  are 
never  so  regular  as  those  of  the  preceding  figure,  since  we 
never  have  a  perfectly  regular  cyclone,  as  assumed  above,  and 
besides  there  are  always  other  abnormal  disturbances  of  tem- 
perature combined  with  those  of  the  cyclone. 

The  air  on  the  east  side  of  a  cyclone,  at  least  near  the  surface 
of  the  earth,  is  very  damp  and  oppressive,  much  more  so  than 
it  was  while  in  the  lower  latitudes  from  which  it  has  been 
drawn  ;  for  as  it  is  carried  up  to  higher  latitudes  over  a  surface 
which  becomes  colder  with  increase  of  latitude,  it  of  course 
cools  down  some,  though  not  nearly  to  the  normal  of  the  lati- 
tude where  the  air  remains  undisturbed,  and  in  this  cooling  it 
becomes  more  nearly  or  quite  saturated.  Exactly  the  reverse 
of  this  takes  place  on  the  west  side.  The  air  found  there  is 
not  only  colder  because  it  has  been  brought  down  from  a 
higher  latitude,  but  it  is  much  drier  than  it  was  in  its  original 
position. 


VEERING   OF  THE   WIND— CHANGES  OF   TEMPERATURE.   287 


VEERING    AND    BACKING    OF     THE    WIND    AND     CHANGES    OF 
PRESSURE  AND   TEMPERATURE. 

192.  If  a  cyclone  remained  stationary  without  any  pro- 
gressive motion,  there  would  be  no  veering  of  the  wind,  and 
the  only  change  would  be  a  gradual  increase  and  then  decrease 
in  its  velocity.  The  barometric  depression,  and  the  tempera- 
ture of  the  interior,  mostly  in  the  upper  strata,  would  be  sub- 
ject to  similar  changes,  and  these  changes  would  have  a  period 
coinciding  with  the  time  of  duration  of  the  cyclone.  But 
where  the  cyclone  has  a  progressive  motion  these  changes  fol- 
low in  more  rapid  succession,  and  complete  their  period  in  the 
time  that  the  cyclone  occupies  in  passing  over  the  place  of 
observation. 

Let  the  arrows  of  the  following  figure  represent  the  direc- 


Fig.  6. 

tions  and  relative  velocities  of  the  wind  in  a  cyclone,  the 
interior  solid  circle  representing  the  line  of  highest  barometric 
pressure  between  the  cyclonic  and  the  anti-cyclonic  gyrations. 
If  the  cyclone  passes  centrally  over  the  place,  say  from  west  to 
^ast,  then  while  the  place  is  in  the  outer  or  anti-cyclonic  part, 
HS  at  a,  there  is  a  very  slight  rise  of  the  barometer  and  a  very 
gentle  wind  from  a  point  west  of  north,  if  there  are  no  abnor- 
mal disturbances.  Then  comes  the  highest  barometric  pressure 
and  the  calm  connected  with  it,  and  when  the  point  b  of  the 
cyclone  has  reached  the  place  of  observation  the  direction  of 


288  CYCLONES. 

the  wind  is  southeasterly,  and  the  velocity  continues  to  increase 
with  little  change  of  direction,  and  the  barometer  to  fall,  until 
the  place  of  observation  relative  to  the  cyclone  is  at  some 
point  c  still  nearer  the  centre,  where  the  cyclonic  motion  is 
most  rapid.  While  the  centre,  and  contiguous  parts  very  near 
on  either  side,  are  passing  over  the  place  of  observation,  there 
is  a  calm,  called  the  "  dead  calm,"  and  the  barometric  pressure 
is  then  the  least.  When  the  progressive  motion  has  continued 
a  little  longer,  until  the  place  of  observation  is  at  dy  there  has 
been  a  complete  change  of  the  wind  to  the  contrary  direction, 
and  the  barometer  is  now  rising,  which  continues  until  the 
opposite  side  of  the  ring  of  high  pressure  and  of  calm  arrives. 
If  the  direction  of  progressive  motion  is  exactly  from  west  to 
east,  the  change  in  the  direction  of  the  wind  at  the  centre  is 
from  about  S.S.E.  to  N.N.W.,  but  if,  as  most  usual  in  the  mid- 
dle latitudes  of  the  northern  hemisphere,  the  cyclone  moves 
toward  the  E.N.E.,  then  the  change,  it  is  readily  seen  from 
the  figure,  must  be  very  nearly  from  S.E.  to  N.W.  At  the 
time  of  this  sudden  change  of  direction  near  the  centre  there  is 
of  course  a  great  and  sudden  change  in  the  character  of  the 
air.  On  the  east  side,  for  reasons  given  in  §  191,  it  is  warm, 
damp,  and  oppressive,  and  this  is  suddenly  changed  to  cold 
and  very  dry  air,  using  the  terms  warm  arid  cold  here  relatively 
to  the  seasons. 

Within  the  tropics,  where  the  direction  of  progressive  motion 
in  the  northern  hemisphere  is  W.N.W.,  the  manner  of  veering 
is  readily  seen  by  placing  the  figure  with  the  line  W.E.  in  that 
direction.  The  directions  of  the  arrows  then  indicate  that  the 
change,  when  the  centre  passes  over  the  place  of  observation, 
is  from  a  northerly  to  a  southerly  direction.  The  same  may 
be  done  for  any  other  directions  of  progressive  motion.  When 
the  place  of  observation,  in  any  case,  is  at  e,  the  violence  of  the 
wind  has  very  much  diminished  and  the  height  of  the  barome- 
ter increased,  and  soon  after  follows  the  highest  barometer 
with  its  accompanying  calm,  after  which  the  usual  light  varia- 
ble winds,  due  to  various  abnormal  disturbances,  are  observed, 
the  normal  inversion  of  direction  again  in  the  anti-cyclonic 


VEERING   OF   THE    WIND— CHANGES  OF   TEMPERA  TURE.  289 

part  being  usually  entirely  obscured  by  these.  If  the  area  of 
central  calm  is  small  and  the  gyrations  are  very  rapid  close  up 
to  the  centre,  as  in  violent  cyclones  of  moderate  dimensions  at 
sea,  then  there  is  a  very  sudden  change  of  a  very  strong  wind 
to  the  opposite  direction. 

If  the  north  side  of  the  cyclone  passes  eastwardly  over  any 
place  of  observation  in  the  northern  hemisphere,  so  that  the 
place  of  observation  occupies  successively  the  places  within 
the  cyclone  m,  n,  and  o,  then  it  is  seen  that  the  change  of  the 
more  violent  winds  in  the  cyclone  proper  is  from  about  E.  at 
m  to  N.E.  at  n  and  then  to  N.  at  o.  In  this  case  there  is  a 
change  of  the  wind  through  only  about  one  quadrant,  and  this 
in  a  direction  contrary  to  the  motion  of  the  hands  of  a  watch, 
called  backing;  but  if  the  south  side  of  the  cyclone  passes  in 
the  same  direction,  over  the  place  of  observation,  so  that  this 
occupies  successively  the  places  /;/',  n' ',  and  o'  in  the  cyclone, 
then  the  change  is  from  S.  at  m'  to  S.W.  at  n',  and  then  to  W. 
at  o',  and  the  change  in  this  case,  through  about  one  quadrant, 
being  in  the  direction  of  the  hands  of  a  watch,  is  called  veering. 

The  direction  in  which  the  wind  changes  depends  entirely 
upon  which  side  of  the  place  of  observation  the  centre  of  the 
cyclone  passes ;  and  the  amount  of  change,  upon  the  distance 
of  the  path  of  this  centre  from  the  place  of  observation.  If 
the  distance  is  small  in  comparison  with  the  dimensions  of  the 
cyclone,  the  change  is  through  about  two  quadrants,  but  with 
greater  distances  the  amount  of  change  is  less.  For  other 
directions  of  progressive  motion,  the  veering  or  backing  of  the 
wind  is  indicated  in  all  cases  by  the  arrows,  when  the  line 
W.E.  is  placed  so  as  to  coincide  with  these  directions. 

The  winds  at  any  given  place  are  liable  to  change  as  fre- 
quently, on  the  average,  in  one  direction  as  the  other,  unless 
the  cyclones  pass  more  frequently  on  the  one  side  of  the  place 
of  observation  than  the  other.  In  the  middle  latitudes  of  the 
United  States  and  of  Europe  cyclones  pass  more  frequently 
on  the  north  side,  so  that  in  these  latitudes  the  change  is  more 
frequently  in  the  same  manner  as  the  motion  of  the  hands  of  a 
watch.  It  was  only  for  this  reason  Dove  found  a  preponder- 


2QO  CYCLONES. 

ance  of  changes  of  this  kind,  in  confirmation  of  his  theory 
with  regard  to  the  rotation  of  the  winds. 

For  the  southern  hemisphere  it  is  only  necessary,  in  what 
precedes,  to  change  N.  to  S.  and  vice  versa,  in  order  to  have 
the  successive  changes  in  the  veering  and  backing  of  the  wind 
in  each  case. 

193.  In  what  precedes  with  regard  to  the  changing  of  the 
directions  of  the  winds,  no  account  is  taken  of  the  effect  of  the 
secondary  conditions  introduced  by  the  action  of  the  cyclone 
itself,  where  there  is  a  considerable  difference  of  the  general 
temperature  on  the  two  sides,  by  which  a  steep  temperature 
and  pressure  gradient  is  introduced  in  an  east  and  west  direc- 
tion between  the  lines  cd  and  ef,  as  represented  in  Fig.  5.  The 
other  component  of  the  gradient  in  a  north  and  south  direction 
remains  much  as  it  was  at  first  before  there  was  any  cyclonic 
disturbance,  and  has  nothing  to  do  with  the  cyclonic  disturb- 
ance, but  simply  with  the  general  easterly  motion  of  the  atmos- 
phere, and  has  already  been  considered  in  a  previous  chapter. 
But  the  other  component  of  the  temperature  gradient  intro- 
duced has  to  be  here  considered  in  connection  with  the  cyclone. 
The  tendency  of  the  cold  dry  air  on  the  west  side  is  to  press 
eastward  below  even  beyond  the  centre  of  the  cyclone,  and  as 
cold  and  warm  portions  of  air  do  not  readily  intermingle,  but 
tend  to  keep  apart,  there  is  often  a  long  line,  several  hundred 
miles  in  length,  in  the  central,  or  perhaps  rather  easterly,  part 
of  the  cyclone,  where  there  is  a  short  but  sharp  temperature 
and  pressure  gradient,  and  where,  in  the  passage  of  a  cyclone 
eastward,  there  is  a  very  sudden  change  of  the  wind  around  to 
some  westerly  or  northwesterly  point,  and  there  may  even  be 
violent  and  simultaneous  squalls,  called  line  squalls,  along  this 
whole  line  with  a  very  sudden  change  of  temperature.  And 
the  general  effect  of  this  east  and  west  temperature  gradient 
on  the  west  side  of  the  cyclone,  beyond  the  line  of  sudden 
transition  from  warm  to  cold  air,  is  to  give  rise  to  a  corre- 
sponding pressure  gradient,  and  so  to  cause  the  wind  to  be  from 
a  direction  more  nearly  west  than  it  would  be  by  a  purely 
cyclonic  motion.  It  is  on  account  of  this  increased  pressure 


VEERING   OF   THE    WIND— CHANGES  OF    TEMPERATURE.  29 1 


gradient  on  the  west  side,  no  doubt,  that  Loomis  obtained  a 
greater  inclination  and  velocity  of  the  wind  in  the  west  than  in 
the  east  quadrant  of  a  cyclone.  His  results  fcr  the  several 
quadrants  were  (Sill.  Jour.,  July,  1874): 


W.  QUADRANT. 

S.  QUADRANT. 

E.  QUADRANT. 

N.  QUADRANT. 

Inclination  
"Velocity  in  miles 
per  hour  

58°  48' 
IO.  I 

49°  35' 
8.8 

32°  6' 

8-3 

47°  27' 
7.6 

The  line  of  sudden  transition  from  warm  to  cold  air,  and 
likewise  of  the  meeting  of  the  southeasterly  and  north- 
westerly winds,  is  a  line  of  minimum  pressure,  and  the  low- 
pressure  area  on  both  sides  is  sometimes  called  a  "  trough." 
It  is  simply  a  great  extension  of  the  central  area  of  low  press- 
ure and  of  calm  of  a  regular  cyclone,  so  that  the  winds,  instead 
of  coming  from  all  sides  in  toward  and  around  the  centre,  come 
in,  not  directly,  but  obliquely,  toward  the  middle  of  the  trough. 
For  this  reason  the  isobars  of  cyclones  in  the  middle  latitudes 
are  not  circular  but  somewhat  elliptical,  with  the  northerly 
part  of  their  longer  axes  corresponding  to  the  trough,  extend- 
ing in  a  direction  a  little  to  the  east  of  north,  as  was  first  dis- 
covered by  Espy,  and  now  more  fully  proven  by  the  researches 
of  Loomis.17  He  found  from  an  actual  measurement  of  the 
greatest  and  least  diameters  of  the  isobars  represented  on  the 
Signal  Service  maps  during  a  period  of  three  years,  that  the 
-average  ratio  of  the  longest  diameter  of  the  isobars  to  the 
shortest  was  nearly  as  two  to  one. 

Since  the  preceding  secondary  effect  depends  upon  differ- 
ences of  general  temperature  in  latitude,  they  occur  principally 
and  most  strikingly  in  the  middle  latitudes  and  in  the  winter 
season,  but  they  may  occur  at  all  latitudes  and  in  all  seasons 
wherever  conditions  are  such,  whether  of  temperature  or  ter- 
restrial radiation,  as  to  cause  a  difference  of  temperature  be- 
tween the  two  sides  ;  for  it  must  be  remembered  that  slight 
differences  of  temperature  and  small  pressure  gradients  give 
rise  to  violent  winds  where  there  are  no  deflecting  forces  arising 
from  the  earth's  rotation  to  counteract  the  forces  of  these 


CYCLONES. 

gradients,  as  in  the  case  of  the  interchanging  motions  in  the 
cases  of  the  vertical  circulations  of  the  atmosphere  and  of 
cyclones.  In  the  lower  latitudes,  however,  where  the  differ- 
ence of  temperature  depending  upon  latitude  is  small,  these 
effects  are  very  small,  and  hence  it  is  said  that  in  the  tropical 
cyclones  there  is  an  "  absence  of  any  marked  squall  or  change 
of  weather  during  the  passage  of  the  trough  in  the  tropics, 
that  is,  at  the  moment  when  the  barometer  begins  to  turn 
upward.50" 

In  the  easterly  progression  of  cyclones  in  the  middle  lati- 
tudes, following  one  another  in  somewhat  regular  succession  at 
intervals  of  a  few  days,  there  is  first  encountered  the  southerly 
winds  on  the  easterly  side  of  the  trough,  and  then,  in  a  few 
days,  the  northerly  winds  on  the  west  side,  and  this  is  frequently 
repeated  at  short  intervals.  This  seeming  struggle,  as  re- 
garded by  Dove,  between  "  equatorial  and  polar  winds,"  now 
so  well  understood,  was  formerly  a  great  mystery  to  the  meteor- 
ologist. 

CYCLONE   OF  AUGUST   2,    1837,    AT   ST.   THOMAS. 

194.  As  an  example  of  some  of  the  theoretical  results 
arrived  at,  we  give  (page  293)  the  observations  of  a  cyclone  at 
St.  Thomas,  made  by  Hoskiaer,  and  copied  here  from  Dove.13 

The  normal  barometric  pressure  here  being  about  29.9 
inches,  the  whole  low-pressure  area,  and  the  part  of  the  cyclone 
having  any  considerable  violence,  passed  over  the  place  of  ob- 
servation in  about  24  hours.  This,  at  the  average  rate  of  15 
miles  per  hour,  at  which  cyclones  progress  here,  would  make 
the  diameter  of  this  part  360  miles,  and  consequently,  accord- 
ing to  Piddington  (§  184),  it  was  not  one  of  the  smallest  kind. 
With  a  barometric  depression  of  nearly  two  inches  in  the  cen- 
tre, even  with  this  area,  the  barometric  gradients  become  very 
large.  Between  6  h.  30  m.  and  7  h.  30  m.  the  change  of  baro- 
metric pressure  was  0.977  in.,  which,  with  the  assumed  rate  of 
progressive  motion,  would  make  a  gradient  of  nearly  one  inch 
in  15  miles.  On  the  opposite  or  rear  side  at  about  the  same 
distance  from  the  centre,  the  gradient  is  less,  being  only  about 


CYCLONE   OF  AUGUST  2,    1837,  AT  ST.    THOMAS.         293 


MEAN 

TIME. 

BAROMETER. 

DIRECTION  OF  THE  WIND. 

h.      m. 

Inches. 

Aug.  i 

18       o 

29.932 

Aug.  2 

2       IO 

•  754 

N.W." 

3     20 

.666 

N. 

3     45 

.666 

N. 

•  Gale  freshening. 

4    45 

.489 

N. 

5     40 

•443 

N.E. 

5     45 

.310 

N.E.  = 

"6     30 

29.133 

N.W. 

•6     35 

28.911 

N.W. 

6     45 
7       o 

•778 
•778 

N.W. 
N.W. 

••  Hurricane. 

7     10 

.600 

N.W. 

7    22 

.289 

N.W. 

7    30 

.156 

N.W. 

7    35 

.in 

7     52 
8     10 

.067 
.067 

Dead  calm. 

8      20 

.067 

8     23 

•423 

S.S.E.' 

8    33 

•511 

S.E. 

8     38 

.600 

S.E. 

8    45 

.689 

S.E. 

8     50 

•778 

S.E. 

9      o 

28.995 

S.E. 

vQ       10 

29.133 

S.E. 

9    25 

.222 

S.E. 

9    35 

•  310 

S.E. 

•  Hurricane. 

9     50 

•399 

S.E. 

IO      IO 

.489 

S.E. 

10    35 

•577 

S.E. 

II       10 

•599 

S.E. 

ii     30 

.621 

S.E. 

14    45 

-754 

S.E. 

20        0 

.888 

S.W. 

2T         0 

29.910 

E. 

O.8  in.  in  15  miles.  These  gradients,  therefore,  are  enormously 
greater  than  the  estimated  gradient  of  the  cyclone  of  the  Fiji 
Islands  (§  186),  although  the  minimum  of  the  depression  in 
this  latter  case  was  much  lower.  But  it  is  seen  that  the  ba- 
rometer, as  usual  in  such  storms,  was  irregular,  being  affected 
by  various  irregular  and  abnormal  disturbances,  so  that  the 
gradients  at  any  given  time  can  be  only  approximately  deter- 
mined. In  the  front  part  of  the  storm  at  7  h.,  taking  the  aver- 
age between  6  h.  30  m.  and  7  h.  30  m.,  it  was  approximately  one 
inch  in  15  miles  or  21  mm.  in  the  distance  of  60  geographical 


294  CYCLONES. 

miles.  Assuming  the  exact  centre  of  the  cyclone  to  be  at  the 
place  of  observation  at  8  h.  10  m.  and  that  the  progressive  ve- 
locity was  15  miles  per  hour,  the  distance  of  that  gradient  from 
the  centre  was  about  17  miles,  or  27  kilometers.  Putting  now 
Gt,  §  57,  equal  to  21  mm.  and  r  —  27.000  meters,  and  /=  18°, 
the  value  of  v  which  satisfies  the  expression  for  a  temperature 
of  30°  C.  is  24  meters  per  second,  or  about  54  miles  per  hour 
for  the  approximate  gyratory  component  of  velocity,  and  as 
the  inclination  in  such  small  and  violent  cyclones  is  small,  even 
in  this  latitude,  this  is  not  much  less  than  the  real  velocity. 
Of  course  this  estimate  is  subject  to  all  the  uncertainties  of 
gradient  and  distance,  where  there  are  so  many  irregularities 
in  the  barometer,  and  where  the  exact  progressive  velocity  is 
not  known. 

By  comparing  the  value  of  v  =  v/r  in  the  preceding  com- 
putation, with  that  of  2n  sin  /  as  deduced  from  Table  V,  it  is 
seen  that  the  former  is  more  than  14  times  greater,  and  hence 
the  gradient  here  in  this  low  latitude  depends  almost  entirely 
upon  the  centrifugal  force  of  the  gyrations,  and  very  little  upon 
the  earth's  rotation. 

As  the  progressive  motions  of  cyclones  in  this  vicinity  are 
in  a  direction  only  a  little  north  of  west,  and  this  cyclone  seems 
to  have  passed  very  nearly  centrally  over  the  place  of  observa- 
tion, by  placing  the  line  W.E.  in  Fig.  6  in  that  direction,  andi 
making  allowance  for  a  greater  inclining  in  toward  the  centre 
in  this  low  latitude  than  that  represented  in  the  figure,  which  is 
more  adapted  to  the  middle  latitudes,  it  is  seen  that  in  the  more 
violent  part  of  the  front  of  the  cyclone,  as  at  the  points  e  and  d, 
the  wind  is  N.W.,  as  represented  in  the  preceding  table  of  ob- 
servations. Then  comes  the  "  dead  calm"  at  the  centre  with 
lowest  pressure,  which  continues  about  45  minutes,  and  so,  with 
a  progressive  velocity  of  15  miles  per  hour,  it  must  have  been 
about  12  miles  in  diameter;  but  of  course  there  is  no  definite 
limit,  since  the  gyrations  at  first  become  merely  perceptible, 
and  then  gradually  increase  with  distance  from  the  centre, 
though  very  rapidly,  so  that  at  only  a  short  distance  they  be- 
come extremely  violent.  At  the  points  c  and  b  in  the  rear 


MANILLA    TYPHOON  OF  NOVEMBER  5,  1882. 


295 


part  there  is  a  complete  change  of  direction  to  the  S.E.,  as 
shown  in  the  preceding  observations,  which  has  taken  place  in 
a  short  time,  while  the  central  calm  passed  over  the  place. 

The  observations,  as  given,  were  not  commenced  soon 
enough,  and  continued  long  enough,  to  indicate  the  belt  of 
high  pressure  and  the  anti-cyclonic  directions  of  the  wind  on  the 
outer  border  of  the  cyclonic  region  of  disturbance,  but  these, 
most  probably,  would  have  been  masked  by  small  abnormal 
disturbances. 


MANILLA  TYPHOON  OF  NOVEMBER   5,  1882. 

195.  This  cyclone  has  been  investigated  by  Loomis,17  and 
the  following  table  of  observations  of  its  central  and  more  vio- 
lent part  is  copied  approximately  from  the  curves  of  his  dia- 
gram. 


TIME. 

BAR.  PRESSURE. 

TEMPERATURE. 

WIND. 

Velocity. 

Direction. 

d.   h. 

mm. 

m. 

4   22 

752 

23° 

6 

N.W. 

23 

52 

23 

10 

N.W. 

5   o 

51 

22 

20 

W.  i  N.W. 

I 

50 

22 

21 

W.N.W. 

2 

48 

22 

30 

W.  i  N.W. 

3 

47 

21 

33 

W.N.W. 

4 

46 

21 

22 

W.N.W. 

5 

46 

21 

34 

W.N.W. 

6 

46 

21 

28 

W.N.W. 

7 

45 

21 

29 

W.N.W. 

8 

43 

21 

36 

W.N.W. 

9 

37 

21 

44 

W.N.W. 

10 

35 

22 

2 

N.N.E. 

ii 

37 

25 

9 

E.  iS.E. 

12 

38 

24 

12 

S-E.  iE. 

13 

43 

26 

25 

S.E.  ±E. 

14 

45 

27 

28 

E.S.E. 

15 

46 

26 

30 

E.  iS.E. 

16 

47 

25 

22 

E.S.E. 

17 

48 

25 

16 

E.S.E. 

If 

49 

25 

15 

E.S.E. 

19 

50 

25 

14 

E.S.E. 

20 

51 

25 

IO 

E.S.E. 

21 

52 

24 

10 

E. 

22 

52 

24 

12 

E.S.E. 

296 


CYCLONES, 


The  minimum  pressure  of  this  cyclone  was  not  very  low  nor 
the  gradients  very  steep,  except  very  near  the  centre,  although 
the  velocities  of  the  wind  were  considerable/  This  is  because 
the  cyclone  was  large  for  this  latitude,  and  the  distances  mostly 
were  much  greater  than  in  the  case  of  the  St.  Thomas  cyclone. 
It  is  seen  from  the  expression  of  £4,  §  57,  that  with  larger  val- 
ues of  r  the  value  of  G  becomes  smaller.  The  sudden  rever- 
sion of  the  direction  of  the  wind  is  explained  as  in  the  pre- 
ceding case.  This  cyclone,  however,  being  a  little  nearer  the 
equator,  the  directions  of  the  wind  seem  to  have  been  more 
nearly  radial,  as  they  should  be,  than  in  the  preceding  case,  so 
that  the  change  is  from  W.N.W.  to  E.S.E.  mostly,  instead  of 
from  N.W.  to  S.E.,  as  in  the  case  of  the  St.  Thomas  cyclone. 
The  duration  of  the  central  calm  seems,  as  usual,  to  have  been 
short. 

If  we  assume  that  5  d.  10  h.  was  the  exact  time  of  the  pas- 
sage of  the  centre,  and  compare  the  several  pressures  and  tem- 
peratures for  each  hour  preceding  and  following  this  passage, 
we  get  the  following  results : 


Hours 
Before  and 

After. 

PRESSURE. 

TEMPERATURE. 

WIND  VELOCITY. 

Before. 

After. 

Before. 

After. 

Before. 

After. 

mm. 

mm. 

I 

737 

737 

21° 

25° 

44 

9 

2 

43 

38 

21 

24 

36 

12 

3 

45 

43 

21 

26 

29 

25 

!        4 

46 

45 

21 

27 

28 

28 

;     s 

46 

46 

21 

26 

34 

30 

6 

46 

47 

21 

25 

22 

22 

!            7 

47 

48 

21 

25 

33 

16 

8 

48 

49 

22 

25 

30 

15 

9 

50 

50 

22 

25 

21 

14 

10 

5i 

5i 

22 

25 

20 

10 

ii 

52 

52 

23 

24 

IO 

IO 

12 

52 

52 

23 

24 

6 

12 

From  this  it  is  seen  that  the  rear  side  of  the  cyclone  is  the 
warmer  side,  and  in  the  passage  of  the  cyclone  the  transition  is 
from  cold  to  warm,  contrary  to  what  occurs  in  the  middle  lati- 
tudes, as  illustrated  by  Fig.  5  and  shown  by  observation  ;  and 
the  isotherms,  if  drawn,  would  curve  down  on  the  front  side 


CYCLONE   OF  CIENFUEGOS  ON  SEPT.    5,  1882. 


297 


toward  the  equator  instead  of  toward  the  pole.  This  is  be- 
cause the  progressive  motion  is  nearly  in  the  contrary  direc- 
tion. The  effect,  however,  is  comparatively  small,  since  in  this 
low  latitude,  even  in  November,  the  difference  of  temperature 
due  to  difference  of  latitude  on  the  two  sides  is  small.  The  cor- 
responding increase  of  pressure  on  the  front  side  on  account 
of  lower  temperature  seems  to  be  only  very  faintly  indicated 
in  the  preceding  table.  In  general  the  wind  velocities  in  the 
preceding  table  are  greater  on  the  front  than  the  rear  side,  but 
this  is  most  probably  due  to  the  winter  monsoon,  which  at  this 
season  is  already  set  in,  and  the  direction  in  this  region  is 
rather  from  the  N.W.,  which  tends  to  increase  the  velocity  in 
front  a  little  and  to  decrease  it  a  little  in  the  rear. 

CYCLONE    OF  CIENFUEGOS  ON  SEPT.    5,    1 882. 

196.  The  following  observations  of  this  cyclone  are  taken 
from  the  Report  of  the  Chief  Signal  Officer  for  1883,  p.  759. 


Time. 

Barometer. 

Temper- 
ature. 

Wind. 

Force. 

State  of  the  Weather. 

d.    h. 

Inches. 

5      ° 

29.82 

82° 

N. 

2 

Clouds  between  i°  and  2°  quadrant. 

2 

29.76 

80 

N.W. 

3 

Heavy  gusts  of  rain. 

8 

.66 

80 

N.W. 

3 

Do. 

9 
9    3^ 

•59 
•  50 

78 
78 

N.W. 
W.N.W. 

4 
4 

Hurricanes,  gusts. 
Violent  gusts  of  wind  and  rain. 

10         0 

•38 

78 

W.N.W. 

4 

Hurricane. 

10    15 

•31 

78 

W.  Yt  N.W. 

4 

Gloomy  and  cloudy  weather. 

10    30 

.27 

78 

w. 

4 

30    45 

.22 

78 

w. 

4 

Greatest  intensity. 

II          O 

ii     30 

.18 
.13 

78 

78 

W.  J4S.W. 

w.s!w. 

4 
4 

Blowing  with  great  force. 
Do. 

11     45 

•15 

78 

s.w.  YI  w. 

4 

Barometer  rising. 

12         0 

.16 

78 

s.s.w. 

4 

I  Gloomy  appearance,  rain  in  tor- 
|     rents. 

12       30 

.18 

78 

s.s.w. 

4 

Do. 

I          O 

.27 

78 

s.s.w. 

4 

Do. 

I       30 

•32 

78 

s.  YA,  s.w. 

4 

Do. 

2         0 

•44 

78 

s.  M  s.w. 

4 

j  Less  wind  gusts  and  of  short  du- 
{     ration. 

2       30 

.46 

78 

s.  Y4  s.w. 

4 

3      o 

.46 

78 

s. 

4 

Gusts  diminishing. 

3     30 
4      o 

•49 

78 
78 

s. 

S.S.E. 

Rapid  gusts. 
Heavy  rain. 

5       ° 

6O 

78 

S.S.E. 

Do. 

6       o 

!66 

78 

S.E. 

Rains  and  gusts. 

7       o 

.70 

78 

S.E. 

Strong  winds  with  lasting  gusts. 

8       o 

.78 

78 

S.E. 

*       Do. 

9       o 

•79 

78 

SE. 

Heavy  rain  and  strong  wind. 

10        O 

.80 

78 

S.E. 

3 

Gusts  at  intervals. 

This  is  an  example  in  which  the  centre  of  the  cyclone  did 
not  pass  over  the  place  of  observation,  but  on  the  north  side. 


298  CYCLONES. 

There  is,  accordingly,  no  dead  calm  and  sudden  change  of  the 
wind  to  the  opposite  direction,  but  a  gradual  backing  of  the 
wind  from  a  N.W.  wind  in  the  front  to  a  S.E.  wind  in  the  rear. 
The  explanation  of  this  is  readily  seen  by  reference  to  the  ac- 
companying figure,  in  which  the  large  arrow  indicates  the  di- 
rection of  progression,  and  the  parallel  line  with  the  small 
arrows  and  the  even  hours  of  the  time  indicates  the  place  of 
observation  at  the  several  times  with  reference  to  the  centre  of 

29-80 


Fig.  7. 

the  cyclone.  The  calm  centre  passed  north  of  the  place  of  ob- 
servation, and  so  when  it  was  nearest,  the  place  of  observation 
was  at  the  distance  of  greatest  violence.  If  the  centre  had 
passed  on  the  other  side  there  would  have  been  a  gradual  veer- 
ing instead  of  backing  of  the  wind. 

RAIN   AND   CLOUD   AREAS   IN   CYCLONES. 

197.  Since  the  air  flows  in  from  all  sides  of  a  cyclone 
toward  the  central  area,  and  consequently  gradually  ascends 
there,  this  must  be  a  region  of  cloud  and  rain,  just  as  the  equa- 
torial belt  is,  where  the  air,  coming  in  from  both  sides  in  the 
lower  strata,  is  deflected  upward  and  becomes  an  ascending 
current.  The  explanation  of  the  formation  of  cloud  and  rain, 
and  the  height  to  which  the  surface  vapor  has  to  ascend  before 
cloud-formation  takes  place,  is  the  same  in  both  cases,  and  has 
been  already  given  (§  in). 

The  rain  and  cloud  areas  do  not  coincide  with,  nor  are  they 


RAIN  AND    CLOUD  AREAS  IN  CYCLONES.  299, 

even  concentric  with,  the  areas  of  low  pressure  and  of  ascending 
currents ;  for  the  ascending  and  partially  condensed  vapor  and 
the  cloud  may  be,  and  generally  is  in  the  middle  and  higher 
latitudes,  carried  eastward  beyond  the  limits  of  the  low  press- 
ure area,  by  the  strong  easterly  currents  above,  into  the  anti- 
cyclonic  area  before  it  falls  as  rain  ;  and  hence  the  centre  of 
the  area  of  cloud  and  rain  falls  considerably  in  advance  of  the 
centre  of  low  pressure  and  of  cyclonic  gyration  in  their  easterly 
progression.  These  areas,  as  those  of  low  pressure,  are  ellip- 
tical, and  not  circular  as  they  would  be  in  case  of  regular  con- 
ditions with  no  greater  progressive  motion  of  the  atmosphere 
above  than  below. 

According  to  Loomis,51  "  the  form  of  these  rain  areas  is. 
sometimes  quite  irregular,  but  generally  it  approximates  to  an 
ellipse  of  which]  the  major  axis  is  not  quite  double  the  minor 
axis."  The  average  distance  of  the  centre  of  rainfall  from  the 
centre  of  low  pressure,  north  of  latitude  36°,  was  found  to  be^ 
300  miles,  but  it  sometimes  exceeded  750  miles.  The  general 
direction  of  the  longer  axis  of  the  rain-area,  and  of  the  centre 
of  this  area  from  that  of  the  area  of  low  pressure,  is  the  same 
as  the  direction  of  the  progressive  motion  of  cyclones.  This 
indicates  that  both  the  former  and  the  latter  depend  mostly 
upon  the  general  motion  of  the  atmosphere.  The  whole  cy- 
clone and  storm  area  drifts  with  the  average  velocity  of  the 
different  strata,  but  the  upper  strata,  in  which  the  vapor  con- 
densation takes  place  mostly,  have  a  greater  average  velocity, 
and  so  the  rain  and  the  cloud  are  carried  forward,  and  the  rain 
falls  mostly  in  the  front  part  of  the  cyclone  in  the  direction  in 
which  the  general  atmosphere  and  the  whole  cyclone  are  mov- 
ing. Of  course  this  is  only  approximately  so,  for  we  have  seen 
(§  189)  that  the  direction  of  the  progressive  motion  may  be 
affected  considerably  by  other  circumstances.  The  direction 
and  distance  of  the  centre  of  rainfall  from  the  centre  of  low 
area  indicates  the  location  of  greatest  energy  in  the  cyclone,, 
and  this,  we  have  seen,  does  not  depend  entirely  upon  the  mere 
drifting  of  the  upper  strata  of  the  atmosphere  where  the  centre, 
of  energy  is. 


3OO  CYCLONES. 

In  general  the  cloud  area,  though  somewhat  concentric  with 
that  of  the  rain  area,  is  very  much  larger ;  for  it  requires  a  con- 
siderable depth  of  cloud  to  give  rise  to  rainfall,  and  so  the 
outer  parts  of  the  cloud,  arising  mostly  from  the  lateral  expan- 
sion of  the  air  in  its  ascent,  and  not  directly  from  the  ascent  of 
air,  are  not  of  sufficient  depth  to  furnish  rain.  In  the  easterly 
progression  of  a  cyclone,  therefore,  there  is  observed  first  merely 
haziness,  then  a  thin  and  light  stratum  of  cloud,  and  then  the 
heavy,  deep  nimbus,  from  which  rain  falls. 

Where  the  conditions  of  a  cyclone  are  such  that  the  vapor 
•of  the  air  is  carried  by  the  ascending  current  in  the  interior  to 
•very  high  altitudes,  where  there  is  a  freezing  temperature,  the 
fine  cirrus  clouds  formed  by  the  freezing  of  the  vapor  there  are 
^carried  eastward  far  in  advance  of  the  cyclone,  by  the  swift- 
moving  easterly  currents  of  these  altitudes  in  the  form  of  fine 
filaments,  which  are  often  so  distorted  by  the  small  whirling 
motions  which  frequently  exist  in  the  atmosphere  as  to  resem- 
ble a  horse's  tail,  and  are  called  "  mares'  tails."  These  cirrus 
^clouds  of  various  forms,  coming  from  a  westerly  direction, 
while  the  hazy  border  of  the  cloud  has  not  yet  made  its 
appearance,  are  generally  precursors  of  a  violent  cyclone  and 
storm  coming  from  that  quarter,  which  may  be  expected  in  a 
few  days. 

198.  It  has  been  shown  (§  156)  that  the  conditions  of  a 
cyclone  are  not  absolutely  dependent  upon  the  condensation 
of  aqueous  vapor.  There  may,  therefore,  be  considerable  cy- 
clonic action  and  barometric  depression,  with  little  or  no  rain- 
fall. If  the  atmosphere  were  entirely  void  of  vapor,  but  was 
in  the  unstable  state  for  dry  air,  from  some  slight  determining 
cause  arising  from  a  small  local  increase  of  temperature  over  a 
considerable  area,  moderate  vertical  and  cyclonic  circulations 
would  ensue,  and  likewise  barometrical  depression  in  the  cen- 
tral part.  Also  where  the  temperature  over  a  considerable 
area  is  considerably  above  that  of  the  surrounding  air,  as  shown 
in  §  159,  it  gives  rise  to  cyclonic  action  of  some  degree  of 
strength,  even  where  the  vapor  is  not  sufficient  to  produce 
>clouds  of  sufficient  depth  and  density  to  give  rise  to  rainfall. 


RAIN  AND   CLOUD  AREAS  IN  CYCLONES.  30  F 

The  energy  of  the  cyclone  is  in  the  condensation  and  not  in- 
the  rainfall,  the  latter  being  only  an  evidence  of  the  former,, 
but  there  may  be  considerable  cloud-formation  without  rainfall. 
In  101  cases  of  low  barometer  in  which  the  depth  of  rain 
did  not  amount  to  one  eighth  of  an  inch,  Loomis51  found  that 
more  than  one  half  showed  a  barometric  pressure  less  than 
29.70  inches ;  more  than  one  third  were  below  29.60  inches, 
and  nearly  one  fourth  of  the  cases  were  below  29.50  inches. 
He  says : 

"There  seems  to  be  no  room  for  doubt  that  barometric  minima  some- 
times form  with  very  little  rain,  and  continue  without  any  considerable 
rain  for  eight  hours,  and  sometimes  for  twenty-four  hours  and  longer. 
These  barometric  minima  seldom  continue  stationary  for  eight  hours,, 
but  almost  invariably  travel  to  the  eastward." 

In  general,  areas  of  low  barometer  are  areas  of  cloud  and 
rain  but  there  is  no  proportionate  relation  between  the  depth 
of  rain,  and  of  barometric  depression,  for  the  latter  depends 
very  much  upon  the  deflecting  force  of  the  earth's  rotation, 
and  the  extent  of  area,  being  the  result  of  an  integration  of  the 
gradient  through  a  distance  from  the  centre,  while  the  former 
depends  mostly  upon  the  velocity  of  the  ascending  currents 
and  the  amount  of  moisture  in  the  air  at  any  given  place,  and 
not  upon  extent  of  area.  Where  considerable  depressions  are 
observed  with  little  or  no  rainfall,  the  cyclonic  action  and  the 
barometric  gradients  are  generally  small,  but  the  depression  is 
considerable  from  the  extent  of  area. 

199.  There  is  a  characteristic  difference  between  tropical 
cyclones  and  those  of  the  middle  and  higher  latitudes.  Aber- 
cromby  says : M 

"  Cirrus  and  halo  appear  all  round  a  tropical  cyclone,  while  they  are- 
never  seen  in  the  rear  of  a  European  storm  ;  and  though  the  way  in 
which  the  rain  seems  to  grow  out  of  the  air  in  front  of  the  cyclone  is  the 
same  everywhere,  the  sky  and  clouds  in  the  rear  of  a  hurricane  are  much 
softer  and  dirtier  than  in  temperate  cyclones.  There  is  not  that  sharp 
difference  between  the  quality  of  clouds  in  front  and  rear  which  is  so 
striking  in  higher  latitudes.  Still  greater  is  the  absence  of  any  marked 
squall  or  change  of  weather  during  the  passage  of  the  trough  in  the 
tropics, — that  is,  at  the  moment  when  the  barometer  begins  to  turn,: 


302  CYCLONES. 

upwards.     Some  who  study  hurricanes  have  scarcely  noticed  any  change 
then  ;  and  all  are  agreed  that  the  trough-phenomena  are  slight." 

According  to  Padre  Viftes"  the  approach  of  cyclones  from 
the  E.  or  S.E.  is  always  indicated  at  Havana  by  the  appearance 
of  cirrus  clouds  while  the  vortex  is  500  miles  or  more  distant, 
and  while  fair  weather  is  yet  prevailing.  The  same  is  also 
observed  as  they  pass  off  at  a  distance.  This  indicates  that 
the  cirrus  clouds  are  observed  on  all  sides  of  the  tropical  cy- 
clones, in  accordance  with  what  is  stated  above.  Again,  ac- 
cording to  Dr.  Doberck,52  at  Hong  Kong  and  in  the  China  Sea 
"  there  does  not  generally  exist  a  fine-weather  area  behind  the 
•cyclone,  as  the  S.  and  particularly  the  S.W.  winds  blow  there 
very  fresh,  accompanied  by  overcast,  damp  and  frequently  wet 
weather.  Thunder-storms  likewise  follow  after  a  typhoon, 
especially  along  the  coast  of  Southern  China." 

In  the  middle  latitudes  the  general  motion  of  the  air  is 
•easterly  at  all  altitudes,  but  its  velocity  is  much  greater  above 
than  below.  Hence  cirrus  clouds  and  halos  never  appear  in  the 
rear  of  cyclones  in  Europe,  or  anywhere  in  the  middle  latitudes. 
Near  the  equator  the  general  motion  of  the  atmosphere  is 
westerly  in  the  lower  part,  and  at  the  season  of  the  year  in 
which  the  tropical  cyclones  mostly  appear,  it  is  so  up  to  a  high 
altitude,  and  above  that  altitude  the  velocity  of  easterly  motion 
is  comparatively  small.  In  this  latitude,  therefore,  the  air 
.ascends  more  nearly  vertically,  and  in  the  expansion  of  the  air 
in  all  directions  as  it  comes  under  less  pressure,  the  vapor  of 
the  ascending  current  is  diffused  somewhat  equally  in  all  direc- 
tions around  the  centre  of  the  cyclone,  so  that  there  is  here  no 
striking  difference  between  the  clouds  in  front  and  rear,  and 
at  Havana  the  cirrus  clouds  are  observed  when  the  cyclone 
centre  is  still  500  miles  or  more  distant  toward  the  east,  and 
while  fair  weather  is  still  prevailing. 

The  reason  the  usual  trough-phenomena  observed  in  higher 
latitudes  in  the  passage  of  a  cyclone  over  a  place  are  not  observed 
in  tropical  cyclones  is  clear  from  what  has  been  stated  with 
regard  to  the  Manilla  typhoon  (§  195).  In  these  there  is  no 
'dose  contact  between  warm  and  cold  air  of  very  different  tern- 


RESULTANTS  OF  CYCLONIC  AND  PROGRESSIVE  MOTIONS.  303 

peratures  and  a  sudden  change  from  the  former  to  the  latter, 
but,  on  the  contrary,  the  change  is  from  colder  air  to  that  which 
is  only  a  little  warmer. 

In  the  higher  latitudes  the  west  side  is  the  clearing-up  side 
of  the  cyclone,  because  the  strong  easterly  currents  above,  es- 
pecially at  high  altitudes,  carry  all  the  vapor  and  cloud  east- 
ward, so  that  soon  after  the  centre  of  the  cyclone  has  passed  a 
place,  the  clouds  mostly  have  passed  it  also,  and  clear  weather 
prevails.  It  is  not  so  in  tropical  cyclones.  Here  the  pro- 
gressive motion  is  westerly,  and  although  the  atmospheric 
currents  below  are  also  westerly  up  to  a  considerable  altitude, 
yet  the  westerly  velocity  decreases  with  increase  of  altitude, 
.and  becomes  easterly  above,  so  that  the  clouds  are  not  driven 
.ahead  in  advance  of  the  cyclone,  but  there  is  enough  of  easterly 
current  above  in  the  cloud  region  to  carry  the  clouds  eastward 
to  the  rear  of  the  cyclone,  and  consequently  there  is  there 
"  overcast,  damp  and  frequently  wet,  weather,"  instead  of  a 
fine-weather  area  such  as  is  observed  in  the  rear  of  cyclones  in 
higher  latitudes. 


RESULTANTS   OF   CYCLONIC   AND   PROGRESSIVE   MOTIONS. 

200.  Where  the  atmosphere  in  which  a  cyclone  exists  has 
.a  progressive  motion  in  some  direction,  as  it  generally  has,  the 
resultant  of  this  and  the  cyclonic  motion  differs  from  the  purely 
cyclonic  motion,  and  the  effect  of  the  progressive  motion  upon 
the  velocity  and  direction  of  the  cyclonic  motion  is  different  on 
different  sides  of  the  cyclone. 

Let  ab,  Fig.  8,  represent  the  velocity  and  direction  of  the 
cyclonic  motion  on  the  several  sides  of  the  cyclone,  with  its 
centre  progressing  a  little  north  of  east,  as  usual  in  the  middle 
latitudes,  and  as  represented  by  the  arrow,  and  also  let  be  rep- 
resent the  velocity  and  direction  of  the  wind  at  the  earth's  sur- 
face, which  may  be  assumed  to  be  the  same,  or  nearly,  in  all 
parts  of  the  cyclone,  and  to  have  very  nearly  the  same  direction 
as  that  of  the  cyclone  centre,  but  its  velocity  is  generally  much 
less.  It  is  seen  from  the  figure  that  the  resultants,  represented 


304  CYCLONES. 

by  ac,  indicate  very  different  velocities  and  inclinations  on  the 
different  sides  of  the  cyclone.  On  the  side  of  the  cyclone  on 
the  right-hand  side  of  the  centre's  path  the  velocity  is  changed 
from  ab  to  ac,  and  is,  therefore,  considerably  increased,  though 
the  direction  is  changed  but  little,  since  the  directions  of  both 
the  cyclonic  and  progressive  motions  are  nearly  the  same.  On 
the  left  hand,  on  the  contrary,  both  the  velocity  and  direction, 
as  represented  by  ac  as  compared  with  ab,  are  very  much 


Fig.  8. 

changed,  the  former  being  decreased  and  the  latter  becoming 
nearly  radial  in  a  direction  toward  the  centre.  On  the  front 
side  the  direction  only  is  very  much  changed,  since  nearly  the 
whole  effect  of  the  progressive  motion  of  the  air  is  upon  the 
direction  of  motion  and  not  upon  the  velocity.  The  inclination 
here,  with  the  assumed  relation  between  progressive  and  cy- 
clonic velocity,  is  negative  or  outward.  In  the  rear  the  effect 
is  an  increase  of  both  velocity  of  the  wind  and  its  inclination 
toward  the  centre. 

Of  course  the  relations  between  the  resultant  velocities  and 
directions  and  those  of  the  cyclonic,  depend  upon  those  be- 
tween the  two  components.  If  the  progressive  velocity  of  the 
air  is  small  in  comparison  with  the  cyclonic,  as  is  usually  the 
case  on  land,  the  cyclonic  velocities  and  directions  are  not 
much  changed,  but  this  is  generally  different  at  sea,  where  the 
progressive  velocity  of  the  air  is  usually  greater.  The  rela- 
tions, as  represented  here  in  Fig.  8,  are  perhaps  those  which 
usually  occur  at  sea,  where  the  progressive  velocity  may  be 
nearly  as  great  as  the  cyclonic. 


RESULTANTS  OF  CYCLONIC  AND  PROGRESSIVE  MOTIONS,  305 

201.  The  progressive  motion  of  the  air  in  the  region  of  the 
West  India  Islands  being  comparatively  large,  its  effect  upon 
both  the  velocities  and  directions  is  quite  large.  Here  the 
trade-winds  become  nearly  east  winds  (§  123).  Hence,  the 
winds  whose  cyclonic  component  of  motion  is  from  the  north 
or  south  suffer  the  greatest  deviation  from  the  original  cy- 
clonic direction,  the  inclination  toward  the  centre  being  de- 
creased where  the  wind  is  from  the  north  and  increased  where 
it  is  from  the  south.  This  will  be  better  understood  from  Fig. 
9,  in  which  ab  represents  the  cyclonic  and  be  the  progressive 


Fig.  9. 

component  of  the  motion  of  the  air  at  the  earth's  surface,  the 
inclination  here  in  these  low  latitudes  being  assumed  to  be 
about  45°.  The  direction  of  progressive  motion  of  the  centres 
of  the  cyclones  here  is  about  W.N.W.,  as  represented  by  the 
arrow  in  the  figure.  It  is  seen  that  in  front  of  the  storm  the 
inclination  of  the  resultant  ac  is  diminished  and  becomes 
nearly  at  right  angles  to  the  radius,  while  in  the  rear  it  is  in- 
creased and  becomes  nearly  radial,  in  consequence  of  the  pro- 
gressive motion  of  the  air  be.  On  the  right-hand  side  the  di- 
rection of  the  progressive  motion  coincides  nearly  with  that  of 
the  cyclonic  motion,  and  hence  the  direction  is  little  changed, 
but  the  velocity  is  greatly  increased  ;  but  on  the  left-hand  side 


306  CYCLONES. 

the  direction  and  velocity  are  both  much  changed,  the  latter 
being  very  small,  since  the  cyclonic  motion  is  somewhat  coun- 
teracted by  the  progressive  motion. 

These  results  are  verified  by  observations  of  the  hurricanes 
of  the  Antilles  of  1875  and  1876.  In  the  hurricane  of  Septem- 
ber, 1875,  it  is  said,42  "the  winds  of  the  anterior  part  of  the 
storm  were  approximately  circular,  or  with  a  slight  inclination 
toward  the  centre  in  some  cases."  But  from  observations 
made  at  numerous  places  "  the  winds  of  the  second  (S.E.) 
quadrant,  which  remained  at  all  these  places  when  the  vortex 
was  at  a  considerable  distance,  suffered  a  great  deviation  to- 
ward the  centre,  and  in  some  cases,  likewise,  the  winds  not  far 
from  the  vortex."  This  large  deviation  is  represented  by  ac 
in  the  rear  part  of  the  storm  in  the  figure.  The  reason  that 
this  great  inclination  occurred  in  some  cases  only  near  the  vor- 
tex, is  that  there  the  cyclonic  component  is  large  and  has  but 
little  inclination,  the  winds  there,  as  we  have  seen  (§  175),  be- 
coming nearly  circular.  Again,  on  the  island  of  Porto  Rico 
"  little  deviation  in  the  winds  of  the  third  and  fourth  (S.W.  and 
N.W.)  quadrants  was  noted,  some  greater  convergency  in 
those  of  the  first  (N.E.)  quadrant,  and  a  great  inclination  to- 
ward the  centre  in  those  of  the  E.  and  S.,  especially  as  they 
became  at  a  great  distance  from  the  vortex." 

Of  the  hurricane  of  the  iQth  of  October,  1876,  it  is  likewise 
said,42 

"After  its  passage  by  Havana  the  winds,  which  in  the  posterior  part 
blew  from  west  to  south,  suffered  a  great  deviation  toward  the  centre, 
and  that  not  only  at  a  distance  from  the  vortex,  but  even  in  its  vicinity." 

And— 

"  The  winds  which  prevailed  from  S.S.E.  to  S.,  and  which,  during  the 
passage  of  the  vortex  by  Havana  blew  with  force  in  the  different  towns 
situated  to  the  E.S.E.  of  Havana,  suffered  likeyise  a  very  notable  incli- 
nation toward  the  centre.  With  respect  to  the  winds  which  prevailed  in 
the  first  quadrant  in  the  different  localities  of  the  anterior  part  of  the 
cyclone,  there  was  observed  in  them  likewise  a  notable  convergency, 
though  in  general  in  a  less  degree." 

It  is  readily  seen  from  a  mere  inspection  of  Fig.  9,  why  on 


RESULTANTS  OF  CYCLONIC  AND  PROGRESSIVE  MOTIONS.  307 

the  Island  of  Porto  Rico  the  winds  had  little  deviation  from 
the  tangent  in  the  S.W.  and  N.W.  quadrants,  that  is,  in  the 
anterior  parts  of  the  cyclone,  and  why  the  inclinations  in  those 
of  the  east  and  south  quadrants  were  great,  especially  at  a 
great  distance  from  the  centre,  where  the  inclination  of  the  cy- 
clonic component  is  large  (§  175). 

Also  why  the  winds  in  the  posterior  of  the  cyclone  of  the 
1 9th  of  October,  after  it  had  passed  Havana,  suffered  a  great 
•deviation  toward  the  centre,  and  the  winds  in  the  region  E.S.E. 
of  Havana,  which  prevailed  from  E.S.E.  to  S.,  suffered  likewise 
a  very  notable  inclination. 

202.  From  what  precedes  it  is  seen  that  the  navigator,  in 
determining  the  direction  of  the  centre  of  a  cyclone  from  the 
direction  of  the  wind,  should,  in  addition  to  considering  lati- 
tude, distance,  from  centre,  and  velocity  (§  181),  likewise  con- 
sider in  what  quadrant  of  the  cyclone  he  is  situated,  since  the 
-direction  of  the  centre  with  reference  to  that  of  the  wind  is  so 
different  in  different  quadrants,  especially  where  there  is  a 
large  progressive  motion  of  the  air,  as  in  the  trade-wind  re- 
gions. In  the  front  part  of  the  cyclone,  where  the  mariner  is 
in  the  greatest  danger,  the  direction  of  the  centre  is  generally 
more  nearly  at  right  angles  to  the  direction  of  the  wind,  and 
consequently  the  old  rules  of  the  circular  theory  are  more 
nearly  correct  here  than  on  any  other  side  of  the  storm  ;  while 
in  the  rear  the  motions  are  more  nearly  radial  in  the  direction 
of  the  centre.  This  difference  between  the  front  and  rear  of 
the  cyclone  is  embraced  in  Dr.  Doberck's  rule  for  the  Philip- 
pine Islands  (§  181). 

It  is  seen  from  Figs.  8  and  9  that  both  in  the  middle  and 
tropical  latitudes  the  velocity  of  cyclonic  motion  is  increased 
on  the  right-hand  side  of  the  path  of  the  centre,  and  decreased 
on  the  left-hand  side,  by  the  progressive  motion  of  the  air  in 
the  neighborhood  of  the  cyclone.  The  right-hand  side,  there- 
fore, in  the  northern  hemisphere  has  long  been  recognized  as 
the  dangerous  side  of  the  cyclone.  In  the  southern  hemisphere 
it  is  of  course  reversed.  In  endeavoring,  therefore,  to  escape 
the  most  dangerous  part  of  the  cyclone,  care  should  be  taken 
"to  avoid  if  possible  this  side. 


308 


CYCLONES. 


203.  But  the  effects  of  the  progressive  motions  of  the  air 
at  a  considerable   altitude  above  sea-level,  on  mountain   tops 
and  in  the  regions  of  the  clouds,  especially  the  cirrus  clouds, 
are  much  greater  than  at  the  surface,  because  the  velocities  of 
progressive  motion  are  much  greater.     In  fact  up  at  the  alti- 
tude of  the   cirrus  clouds   the  progressive  component  is  usu- 
ally the  principal  one,  and  the  cyclonic  merely  causes  considera- 
ble perturbations  in   the  strong  easterly  current  of  these  re- 
gions.    This  is  seen  from  the  results  deduced  from  the  obser- 
vations of  the  cirrus  clouds  made  at  Zi-ka-wei,  as  given  in  §  83. 
From  these  it  is  seen  that  the  motions  are  mostly  from  a  west- 
erly direction,  the  cyclonic  component  being  merely  sufficient, 
for  the  most  part,  to  cause  deviations  of  one  or  two  points  from 
this   direction,  and    rarely   sufficient    to    entirely  reverse  this 
strong  easterly  current  and  give  rise  to  a  motion  from  an  east- 
erly direction.     And  this  is  in  accordance  with  the  estimates 
made  by  Mr.  Ley  from  his  early  observations  on  the  motions 
of  the  cirrus  clouds.     He  states  that  the  most  elevated  ones 
not  uncommonly  traverse  a  distance  of  120  miles  in  an  hour. 
This  is,  no  doubt,  when  the  great  easterly  motions  of  the  air 
in  these  regions  coincide  in  direction  with  a  great  cyclonic  mo- 
tion, as   in   the   S.  or   S.E.  quadrant.     On  the  other  hand,  he 
states  that  calms  are  uncommon  in  this  elevated  stratum,  and 
that   he    observed    only   twice    an    actually   motionless   cirrus 
cloud.46     In  these  cases  the  observations,  no  doubt,  were  made 
in  the  N.  and  N.W.  octant  of  a  cyclone  region,  where  the  cy- 
clonic and  progressive  motions  very  nearly  or  quite  counteract 
each  other. 

204.  Professor  Loomis'  discussion  of   observations   of  the 
Signal  Service,  made  on  the  top  of  Mount  Washington  at  the 
times  of  low  barometer,  gives  the   following  velocities  and  in- 
clination of  the  wind  :53 


West 
Quadrant. 

South 
Quadrant. 

East 
Quadrant. 

North 
Quadrant. 

Velocity  in  miles  
Inclination  

49 
55°  7' 

44 
—  13°  25' 

-5^.44' 

69°354' 

JRESULTANTS  OF  CYCLONIC  AND  PROGRESSIVE  MOTIONS.  309 

Fig.  10  is  a  copy  of  his  graphic  representation  of  the  direc- 
tions of  the  resultants.  Comparing  this  with  Fig.  8,  which 
may  be  regarded  as  a  representation  of  the  resultant  motions 
usually  at  the  surface  of  the  ocean,  it  is  seen  that  the  results 
are  somewhat  similar,  but  the  effect  of  the  progressive  motions 
upon  the  directions  of  the  cyclonic  are  more  striking,  the  in- 
clination in  the  front  part  of  the  cyclone  being  outward  or 
negative.  But  the  resultant  velocity  deduced  from  these  results 
is  from  N.  65°  W.  28  miles  per  hour,  while  in  Fig.  8  the  direc^ 
tion  of  progressive  motion  was  assumed  to  be  from  a  point  a 
little  S.  of  W.  If  we  assume  that  the  cyclonic  velocity  on  the 
average  was  30  miles  per  hour  and  the  inclination  at  this  alti- 


Fig.  10.  Fig.  II. 

tude  10°,  the  results  of  such  an  assumption  with  the  progressive 
•velocity  and  the  direction  given  above  are  represented  by  Fig. 
ii.  By  comparing  this  with  the  preceding  figure,  it  is  seen 
that  the  results  are  very  nearly  the  same,  and  so  are  accounted 
for  by  a  cyclonic  motion  as  assumed  above. 

In  cyclonic  motions  at  a  considerable  altitude  the  inclination 
is  outward  and  not  inward,  as  represented  in  Fig.  8  ;  and  so  for 
the  same  velocities  of  progressive  motion  the  inclination  of 
the  resultant  ac  in  front  is  greater  and  in  the  rear  less  above 
than  at  the  earth's  surface. 

205.  We  come  now  to  the  examination  of  the  results  ob- 
tained by  Mr.  Ley  from  observations  of  the  upper  currents 
already  given  in  the  table  of  §  180.  From  a  mere  inspection  of 


CYCLONES. 

the  angles  given  in  this  table  for  the  several  districts  it  is 
readily  seen  that  they  result  from  a  cyclonic  motion  with  a. 
considerable  outward  inclination,  combined  with  a  large  pro- 
gressive motion  in  the  direction  of  the  progress  of  the  area 
of  depression,  or  nearly  so,  represented  by  the  large  arrow 
in  Fig.  3.  Let  A,  B,  C,  etc.,  in  Fig.  12  represent  the  cen- 
tres of  the  several  octants  in  Fig.  3,  and  let  Aa,  Ba,  Cay 
etc.,  represent  the  velocities  of  cyclonic  motion,  having  an 
outward  declination  of  about  30°;  and  also  ab  represent  the 
velocity  of  progressive  motion  of  the  upper  atmosphere  in  the 
direction  of  the  motion  of  the  centre  of  low-pressure  area,  rep- 


Fig.  12. 

resented  by  the  arrow,  and  let  us  also  suppose  that  this  lat- 
ter velocity  is  very  nearly  equal  to  that  of  the  cyclonic  velocity 
Aa,  Ba,  Ca,  etc.  The  resultants  will  then  be  represented  by 
Ab,  Bb,  Cb,  etc.  It  is  readily  seen  that  the  effect  of  the  pro- 
gressive component  is  to  increase  the  angles  with  the  radius  in 
the  front  and  to  diminish  them  in  the  rear.  The  effect  is 
similar  to  that  on  Mt.  Washington  represented  in  Fig.  10. 
It  is  seen  that  the  largest  angles  with  radius  are  in  the  dis- 
tricts B,  C,  and  D,  and  the  smallest  those  of  F,  G,  and  H.  By 
a  reference  to  the  column  of  "  Mean  angles  with  radius"  in 
the  table  of  §  180,  it  is  seen  that  this  is  very  nearly  the  case, 
there  being  two  exceptions  in  the  inner  districts,  in  which  the 
maximum  in  front  and  the  minimum  in  the  rear  seem  to  be  a 
little  more  toward  the  north  and  south  sides  respectively.  In 


THE  EYE   OF   THE   STORM.  311 

vague  observations  of  this  sort  it  cannot,  of  course,  be  expected 
that  any  hypothesis  would  give  a  nice  agreement  with  obser- 
vation in  quantitative  results. 

It  is  seen  from  Fig.  12  that  the  resultant  velocity  in  the 
octant  A  is  very  small,  and  consequently  the  average  angle 
from  observation  very  uncertain.  In  fact,  the  progressive 
velocity  so  nearly  counteracts  the  cyclonic,  that  this  must  be 
a  district,  on  the  average,  of  calms  rather  than  of  currents. 
This  is  in  accordance  with  the  observations  of  Mr.  Ley,  who 
with  regard  to  this  district  remarks  that  "  the  upper  current, 
which  had  previously  nearly  coincided  in  direction  with  the 
trajectory,  presently  changes,  as  a  rule,  to  a  nearly  opposite 
point,  having  just  before  become  very  slow.  In  the  interval 
the  cirrus,  when  visible,  which  is  rarely  the  case,  is  sometimes 
stationary,  sometimes  moves  towards,  and  sometimes  from, 
the  centre  of  depression,  these  three  instances  being  nearly 
equally  common,  but  calms  and  motions  toward  the  centre 
predominating."  40 

THE   EYE   OF  THE   STORM. 

206.  In  all  parts  of  the  world  there  appears  to  be  in  the 
central  part  of  most  at  least,  if  not  all,  cyclones  a  thinning 
of  the  cloud-stratum  and  a  partial,  and  sometimes  complete, 
clearing  away  of  the  clouds.  This  was  observed  by  Dove  at 
Konigsberg  as  early  as  the  year  I82/.13  He  says: 

"  Whenever  the  equatorial  current  sets  in  suddenly  and  is  as  sud- 
denly displaced  again,  at  the  precise  time  when  the  barometer  is  at  its 
lowest  level,  the  showers  which  belong  to  the  equatorial  current  are 
separated  from  those  produced  by  the  intrusion  of  the  polar  current 
into  it  by  a  short  period  of  clear  weather,  to  which  I  gave  the*  name  of 
'clear  interval.'  At  the  centre  of  a  cyclone,  when  the  barometer  is 
lowest,  a  similar  fine  moment  is  so  frequently  observed  that  sailors  have 
given  it  a  special  name,  '  the  eye  of  the  storm.'  Captain  Salis  describes 
its  occurrence  in  a  cyclone  experienced  by  the  ship  Paquebot  des  Mers  du 
Sud,  in  latitude  38°  S.,  longitude  22°  E.,  in  these  words  :  '  While  there 
was  a  dense  bank  of  clouds  all  round  us,  the  sky  over  our  heads  was 
quite  clear,  so  that  we  could  see  the  stars,  one  of  which,  right  over  the 
head  of  the  foremast,  was  so  bright  that  every  one  on  board  noticed  it. 
The  barometer  was  27.79  inches  English.'  " 


312  CYCLONES. 

Dove  here  has  in  mind  the  old  idea  of  a  constant  wrestling- 
between  equatorial  and  polar  winds,  and  makes  a  distinction 
between  what  he  observed  and  what  is  seen  in  the  central  part 
of  tropical  cyclones.  But  in  fact  he  simply  observed  what  oc- 
curred in  the  passage  of  the  centre  of  cyclones,  modified  how- 
ever in  high  latitudes  by  the  trough-phenomena  (§  193). 

The  following  quotation  taken  from  an  account  of  a  cyclone 
in  the  Arabian  Sea,  by  Dr.  Malcolmson,  is  given  by  Pid- 
dington  : 

"  During  the  height  of  the  storm  the  rain  fell  in  torrents,  the  lightning 
darted  in  awful  vividness  from  the  intensely  dark  masses  of  clouds  that 
pressed  down,  as  it  were,  on  the  troubled  sea.  In  the  zenith  there  was 
'visible  an  obscure  circle  of  imperfect  light  of  ten  or  twelve  degrees." 

With  regard  to  the  cyclone  of  October,  1848,  in  the  Bay  of 
Bengal  Piddington  further  says  : 

"The  superintendent  of  the  light-house  at  False  Point,  Palmiras, 
distinctly  states  that  at  the  time  of  the  passage  of  the  centre,  or  for 
about  two  hours  of  calm,  the  stars  were  seen  very  clear  overhead,  with  a 
thick  bank  of  haze  all  round." 

This  feature  of  cyclones  seems  to  belong  mostly  to  tropical 
latitudes.  Abercromby &0  says : 

"  The  tropical  cyclone  has  a  striking  feature  which  is  absent  in  our 
latitudes  :  There  is  a  patch  of  blue  sky  over  the  calm  centre,  which  is 
well  known  in  hurricane  countries  as  the  '  eye  of  the  storm,' or  as  a 
'  bull's-eye/  " 

From  the  fact  that  it  was  noticed  by  Dove,  the  phenome- 
non does  not  seem  to  be  entirely  absent  in  higher  latitudes, 
though  it  is  undoubtedly  less  distinctly  manifested  than  in 
tropical  latitudes ;  and  the  name  is  not  so  appropriate  as  it  is 
in  the  case  of  the  small  tropical  cyclones  in  which  the  clear 
patch  seems  to  be  small  and  often  very  distinct,  and  which 
consequently  gave  origin  to  the  name. 

Every  one  perhaps  has  observed  in  ordinary  rain-storms  that 
after  it  has  rained  for  some  time  there  is  frequently  a  cessation 
of  rain  at  least,  if  not  a  partial  clearing  away  of  clouds,  as 
though  the  storm  had  all  passed  by ;  but  after  a  short  time 


THE   EYE   OF   THE   STORM.  313 

there  is  a  thickening  and  a  darkening  of  the  clouds  and  a  sec- 
ond shower  of  rain.  Indeed,  of  so  frequent  occurrence  is  it 
that  it  is  generally  remarked  that  the  latter  is  the  "  clearing-up 
shower,"  as  though  it  were  a  matter  of  course,  and  to  be  ex- 
pected before  the  final  clearing  away. 

207.  The  origin  and  explanation  of  these  phenomena  are 
to  be  found  in  temperature  conditions,  such  as  assumed  in  the 
table  of  §  159,  which  give  rise  to  a  vertical  circulation  which 
does  not  extend  to  the  top  of  the  atmosphere,  often  to  a  mod- 
erate height  only,  and  which,  except  so  far  as  it  acts  upon  the 
upper  part  of  the  air  by  friction  merely,  gives  rise  to  cyclonic 
motion  in  the  lower  strata  only.  It  was  the  opinion  of  Red- 
field  that  our  great  revolving  storms  do  not  generally  extend 
to  a  greater  altitude  than  a  mile,  and  this  is  no  doubt  some- 
times the  case ;  for  the  cirrus  clouds  sometimes  seen  through 
an  opening  of  the  lower  clouds,  the  eye  of  the  storm,  fre- 
quently appear  to  be  undisturbed  by  the  storm  beneath.  But 
at  other  times,  we  know, — and  this  is  frequently  the  case, — the 
highest  cirrus  clouds  are  brought  into  the  whirl,  and  have  a  cy- 
clonic motion.  If  the  conditions  are  such  in  the  upper  part  of 
the  atmosphere  that  the  ascending  current  becomes  colder  in- 
stead of  warmer  than  the  surrounding  part  of  the  atmosphere, 
of  course  it  ceases  to  ascend  and  is  deflected  off  horizontally  in 
.all  directions  before  reaching  that  level.  As  the  gyratory  mo- 
tion depends  upon  the  vertical  circulation,  this,  at  least  at 
first,  extends  up  to  this  level  only,  but  the  strata  above  may  be 
acted  upon  more  or  less  by  friction.  The  air,  charged  with 
.moisture,  in  its  vertical  circulation,  in  toward  the  centre  below, 
up  in  the  interior  to  a  given  altitude,  and  outward  above  in 
the  middle  strata,  necessarily  moves  in  a  path  somewhat  ellip- 
tical ;  so  that  it  is  being  deflected  outward  above  and  still 
ascends  until  at  a  considerable  distance  from  the  centre  ;  and  so 
there  is  little  condensation  of  vapor  in  the  central  part,  and  the 
cloud  stratum  is  thin,  sometimes  entirely  wanting.  And  this 
state  is  still  further  promoted  by  the  gyratory  motion,  which  is 
confined  mostly  to  the  lower  and  middle  strata,  bringing  the 
.air  down  from  above,  it  may  be,  down  pretty  low,  into  the'  inte- 


CYCLONES. 

rior  central  part,  where  it  is  carried  out  horizontally  on  alP 
sides  ;  and  the  descending  air  in  the  interior  above  is  of  course 
clear  air.  The  effect  under  such  conditions  is  a  thinning  of 
the  cloud  and  a  scantiness  of  condensation  and  rainfall  in  the 
centre,  a  ring  of  deeper  and  denser  cloud  at  some  distance 
from  the  centre,  which  gradually  shades  off  to  the  outer  limit. 
Where,  however,  the  conditions  give  rise  to  a  vertical  or  cy- 
clonic circulation  up  to  very  high  altitudes,  this  phenomenon 
is  perhaps  never  observed. 

The  tendency  of  the  air  in  the  interior  of  a  cyclone  to  set- 
tle down,  and  thus  to  either  partially  hinder  the  ascending  cur- 
rents and  the  cloud-formation,  and  so  to  cause  a  thinning  of 
the  cloud,  or  to  even  cause  a  gently  descending  current  and  a 
complete  clearing  off  here,  is  no  doubt  caused  often  by  the  fall- 
ing of  a  great  amount  of  comparatively  cold  rain  from  the  upper 
strata,  which,  both  from  its  weight,  which  is  partially  sustained 
by  the  air  in  falling,  and  also  from  the  cooling  effect,  increases* 
the  downward  pressure  in  the  centre.  And  this  would  espe- 
cially be  the  case  in  tropical  cyclones,  where  the  air  ascends: 
more  vertically  and  symmetrically  on  all  sides,  and  the  rain  is; 
not  mostly  carried  away  in  front  of  the  centre  before  it  falls. 
Hence  the  central  partially  or  wholly  clear  space  is  mostly 
observed  in  these  cyclones. 

In  the  regular  progression  of  a  cyclone  in  the  middle  lati- 
tudes somewhat  centrally  over  a  place,  the  cloud  and  rain  area 
of  the  front  part,  extending  far  toward  the  east,  first  passes- 
over,  occupying  a  half-day,  or  a  day  and  more,  and  then  the 
front  part  of  the  ring  of  dense  cloud  with  a  heavy  shower  of 
rainfall.  After  this  there  are  indications  of  a  clearing  up,  and 
even  the  sun  may  break  through  the  cloud  for  an  hour  or  two  ; 
but  presently  there  is  an  apparent  gathering  and  thickening  of 
the  cloud  and  a  second  shower.  This  is  at  the  time  of  the 
passage  of  the  rear  side  of  the  ring  of  denser  cloud.  After 
this  there  is  the  final  clearing  up. 

It  is  not  to  be  supposed  that  this  is  a  regular  occurrence  in* 
every  rain-storm,  or  that  the  cloud  ring  in  the  special  cases  of 
favorable  conditions  is  regularly  formed  on  all  sides,  but  simply 


SECONDARY  CYCLOXES.  31$, 

that  in  general  the  tendency  is  toward  the  formation  of  such  a 
ring. 

SECONDARY   CYCLONES. 

208.  It  often  happens  that  the  conditions  of  a  smaller 
cyclone,  such  as  described  in  §  157,  or  even  several  of  them,  are 
contained  within  the  limits  of  a  larger  one.  The  isobars  then, 
which  in  a  perfectly  regular  cyclone  are  circular,  become  very 
irregular.  The  contained  cyclone  may  be  such  as  to  give  a  sec- 
ondary minimum  pressure,  or  it  may  simply  produce  derange- 
ments in  the  regularity  of  the  isobars  of  the  primary  cyclone. 
Where  the  isobars  become  crowded,  and  consequently  the  baro- 
metric gradients  steeper,  the  velocities  are  likewise  greater ;  for 
in  such  places  the  motions  of  the  primary  and  secondary  cy- 
clones are  somewhat  in  the  same  direction.  Where,  however, 
the  isobars  are  farther  apart,  and  the  gradients  consequently 
smaller,  the  velocities  are  also  smaller,  since  there  the  motions 
are  nearly  in  contrary  directions,  and  partially  or  quite  neutral- 
ize each  other. 

Fig.  13  represents  the  effects  of  secondary  cyclones  con- 
tained in  a  primary,  upon  the  isobars  and  the  directions  of  the 
wind.  In  the  one  on  the  left  the  depression  is  not  sufficient  to 
give  rise  to  a  secondary  minimum  of  pressure,  but  merely  to 
cause  considerable  derangement  of  the  isobars,  crowding  them 
together  on  the  one  side*  and  widening  them  on  the  other,  and' 
changing  somewhat  the  velocities  and  directions  of  the  wind. 
The  one  on  the  right  being  more  violent  and  the  depression 
deeper,  produces  a  secondary  centre  of  low  pressure,  with 
the  wind  blowing  around  it,  but  with  much  greater  velocity  on 
the  right  side,  where  the  directions  of  the  currents  of  both  the 
larger  and  the  smaller  cyclone  coincide,  than  on  the  other  side 
where  the  cyclonic  motion  of  the  smaller  cyclone  is  but  little 
greater  than  that  of  the  larger  in  the  contrary  direction.  The 
ring  of  high  barometer  of  the  large  cyclone  is  increased  in- 
height  in  an  irregular  manner  by  those  of  the  smaller  ones  fall- 
ing upon  it.  There  are  usually  many  smaller  secondaries  of 
this  sort,  which  tend  to  distort  the  isobars,  and  to  cause  irregu- 


CYCLONES. 


larities  in  the  velocities  and  directions  of  the  wind  as  the  cy- 
clone and  its  secondaries  pass  over  any  place  of  observation. 

Secondary  cyclones  occur  mostly  in  the  southern  and  east- 
ern quadrants  of  a  cyclone,  in  which  the  air  is  warmer  and 
moister  than  in  the  other  quadrants,  and  where  consequently 
-the  conditions  are  more  favorable  for  the  origination  and  main- 


Fig.  13. 

'tenance  of  these  smaller  cyclones.     They  are  rarely,  if  ever, 
found  in  the  other  quadrants. 

209.  Of  course  each  secondary  cyclone  gives  rise  to  an  area 
of  more  dense  cloud  and  more  abundant  rainfall  within  the 
large  one.  The  amount  of  rainfall,  therefore,  in  a  large  cyclone 
may  be  very  unequally  distributed,  large  amounts  of  rain  fall- 
ing in  some  places,  while  at  others  at  no  great  distance  off,  lit- 
tle or  none  falls.  In  fact,  the  larger  cyclone  may  be  such  as 
to  give  rise  to  cloudiness  mostly,  and  to  little  or  no  rain,  while 
there  are  numerous  small  secondaries  contained  within  it, 
which  cause  heavy  rainfalls  over  limited  areas.  In  the  pro- 
gressive motion  of  a  primary  cyclone,  with  its  numerous  small 
secondaries,  each  one  of  the  latter,  as  it  arrives  at  any  place, 


SECONDARY  CYCLONES.  317- 

causes  an  increase  in  the  density  and  darkness  of  the  clouds, 
with  a  shower  of  rain  of  longer  or  shorter  duration,  and  greater 
or  less  abundance,  after  which  the  general  cloudiness,  or  per- 
haps very  moderate  rainfall,  prevails  until  a  new  secondary 
arrives,  when  the  same  thing  occurs  again.  Such  weather  is 
called  showery  weather.  After  the  whole  of  the  large  cyclone 
has  passed  over,  the  showers  cease  and  the  weather  for  a  while 
becomes  settled. 

While  all  areas  of  low  barometer,  whether  of  primary  or 
secondary  cyclones,  are  generally  areas  of  more  or  less  rainfall,. 
or  at  least  of  cloudy  weather,  it  is  not  to  be  supposed  that 
there  may  not  be  much  cloudy  weather  and  rain  without  any- 
sensible  barometric  depression.  The  atmosphere  over  a  large 
area  of  the  earth's  surface  may  be  nearly  saturated  with 
aqueous  vapor,  and  nearly  or  quite  in  a  state  of  unstable  equi- 
librium, and  yet  the  temperature  conditions  may  not  be  such 
as  to  give  rise  to  a  vertica.1  and  a  cyclonic  circulation  over  an 
area  sufficiently  large  to  cause  a  sensible  depression  in  the 
middle,  and  yet  the  vertical  circulation  and  the  ascension  of 
moist  air  may  be  sufficient  to  give  rise  to  much  rain.  For  it 
must  be  remembered  that  a  barometric  depression  depends, 
not  only  upon  gyratory  circulation,  but  also  upon  extent  of 
area,  and  where  the  area  is  small,  the  barometric  depression 
becomes  sensible  only  in  the  case  of  rapid  gyrations,  to  which 
the  conditions  may,  or  may  not,  give  rise.  When  the  atmos- 
phere is  in  the  condition  described  above  there  are  often  many 
local  rains,  with  little  cyclonic  action,  and  consequently  little 
wind,  or  damp,  sultry  weather  may  prevail  with  little  or  no  rain. 
But  if,  after  a  time,  the  temperature  conditions  become  such 
as  to  cause  an  initial  inflowing  of  air  over  a  large  area  toward 
some  central  point,  and  a  vertical  and  cyclonic  circulation 
over  this  area,  this  gives  rise  to  a  cyclone  ot  considerable  ex 
tent,  and  when  this,  by  its  usual  progressive  motion,  has  passed 
away  in  a  day  or  two,  the  damp  drizzly  weather  is  changed 
and  followed  by  fair  weather. 


3 1 8  CYCLONES. 

f 

STATIONARY   CYCLONES. 

210.  If,  for  some  reason,  there  is  a  local  and  permanent 
-cause  of  temperature  disturbance  between  the  central  and 
exterior  part  of  any  somewhat  circular  portion  of  the  atmos- 
phere, we  have  the  conditions  of  a  cyclone  which  is  indepen- 
dent of  the  state  of  unstable  equilibrium,  but  which  would  be 
aided  and  strengthened  by  such  a  state.  The  cause  of  the  tem- 
perature disturbance  being  fixed,  of  course  the  cyclone  cannot 
have  a  progressive  motion. 

The  rough  approximate  conditions  of  such  a  cyclone  are 
found  in  the  northern  part  of  the  North  Atlantic  Ocean,  where 
there  is  a  large  area  over  which  the  temperature  is  higher  than 
that  of  the  surrounding  parts,  and  this  is  especially  the  case  in 
the  winter  season.  The  central  part  of  this  area  of  higher 
temperature  is  near  Iceland,  where  the  mean  annual  temper- 
ature is  about  16°  F.  above  the  normals  of  latitude  for  the 
year,  given  in  the  table  of  §  68.  In  January,  however,  the 
temperature  on  the  continents  in  these  latitudes  has  become 
very  much  less,  while  that  of  the  ocean  has  changed  but  little, 
so  that  at  that  time  the  abnormals  of  temperature  are  at  least 
twice  as  great,  and  likewise  the  difference  between  the  temper- 
ature of  this  area  and  that  of  the  surrounding  parts  of  the 
atmosphere,  so  that  now  we  have  the  conditions  of  a  cyclone  of 
about  twice  as  much  energy  as  in  the  case  of  the  average  for 
the  year,  or  during  the  spring  and  fall.  But  in  July  the  reverse 
takes  place  ;  there  is  then  an  equalizing  somewhat  of  the  tem- 
peratures in  all  longitudes,  and  the  abnormals  of  temperature 
are  very  small. 

Similar  conditions  are  found  in  the  northern  part  of  the 
North  Pacific  Ocean,  but  not  so  marked.  The  greatest  abnor- 
mal temperature  for  the  mean  of  the  year  is  only  about  8°  F., 
and  that  for  January  a  little  more  than  twice  as  much.  Hence 
in  the  northern  parts  of  both  the  Atlantic  and  Pacific  Oceans 
we  have  roughly  the  conditions  of  a  permanent  cyclone  at  all 
seasons  except  the  summer  season,  the  effects  of  which  upon 


STATIONARY  CYCLONES.  319 

the  winds  and  the  barometric  pressures  of  these  regions  are 
observed,  especially  during  the  winter  season. 

In  the  North  Atlantic  Ocean  the  cyclonic  winds  on  the 
southern  side  of  this  great  and  permanent  cyclone  in  winter, 
with  its  centre  near  Iceland,  coinciding  in  direction  with  the 
general  westerly  winds  of  these  latitudes  on  the  Atlantic  Ocean, 
produce  unusually  strong  westerly  winds  at  this  season  ;  but 
adjacent  to  Great  Britain  and  the  coast  of  Norway  they  come 
more  from  a  southwesterly  direction,  and  then,  curving  around 
toward  the  extreme  northern  part  of  the  ocean,  and  on  the 
northern  side  of  the  cyclone,  in  Greenland  and  adjacent  to  it 
on  the  ocean,  the  winds  are  from  the  N.E.  This  cyclonic 
motion  causes  a  barometric  depression  in  the  centre  in  winter 
of  about  10  mm.  below  the  normal  mean  pressure  of  the  lati- 
tude. 

In  the  summer  season  the  temperature  of  that  region  is  so 
nearly  the  same  as  that  of  the  surrounding  regions,  and  of  the 
normal  temperature  of  latitude,  that  there  is  no  sensible  cy- 
clonic action  or  barometric  depression,  and  the  winds  which 
prevail  there  are  the  westerly  winds  of  the  general  motions  of 
the  atmosphere  in  these  latitudes. 

211.  In  the  region  of  the  cirrus  clouds  above  the  winter 
cyclone  of  the  lower  strata  of  the  atmosphere  over  the  North 
Atlantic  Ocean,  the  motion  of  the  air,  in  the  exterior  part  at 
least,  is  anti-cyclonic,  and  consequently  over  the  British  Isles 
and  Europe  generally  the  winds  have  a  considerable  north 
component,  which,  combined  with  the  large  east  component 
of  the  general  motion  of  the  atmosphere  at  high  altitudes, 
causes  their  directions  to  be  from  a  point  more  to  the  N.  of  W. ; 
while  in  the  summer  season,  when  there  is  little  or  no  cyclonic 
effect,  the  general  westerly  winds  at  high  altitudes  are  not 
sensibly  disturbed.  There  is,  therefore,  an  annual  inequality 
in  the  observed  directions  of  the  cirrus  clouds  over  these  re- 
gions, the  directions  being,  according  to  theory,  from  a  point  a 
little  more  to  the  N.  of  W.  in  winter  than  in  summer.  This  is 
found  to  be  the  case  from  observation.  Taking  the  averages 


320 


CYCLONES, 


of  the  angles  $  for  each  month,  given  by  the  late  J.  A.  Brown, 
§  1 80,  we  get : 

October— April,      i/>  =  284° 
,  May— September,  t/>  =  268°. 

Hence  it  is  seen  that  during  the  summer  half  of  the  year  the 
currents  are  almost  exactly  from  the  west,  as  they  should  be, 
for  if  entirely  undisturbed  by  the  anti-cyclonic  action  they 
should  be  from  a  point  a  little  S.  of  W.,  since  the  motion  of 
the  atmosphere  above  is  slightly  poleward.  But  during  the 
winter  half  year  they  are  from  a  point  1 6°  more  toward  the 
north,  because  now  there  is  a  northerly  component  arising  from 
the  anti-cyclone  of  the  cirrus  regions. 

A  similar  result  has  been  obtained  from  observations  made 
on  the  upper  clouds  at  many  places  in  Europe,  by  Dr.  Hugo 
Hildebrand  Hildebrandsson.66  His  results  are  contained  in 
the  following  table  : 


ZONES. 

WINTER. 

SUMMER. 

YEAR. 

Below   760  mm.  (minimum) 
Above  760  mm.  (maximum) 

W.    7°  42'  N. 
W.  42    12   N. 

W.  11°  30'  S. 
W.  23    24  N. 

W.      2°  24'  S. 

W.  31      o  N. 

Mean   

W.  16    54  N. 

W.    3    24  N. 

W.  10    54   N 

Taking  the  general  mean,  we  find  that  the  direction  in  win- 
ter is  from  a  westerly  point  13°  30'  more  toward  the  north  in 
winter  than  in  summer,  and  that  in  the  latter  season  it  is  very 
nearly  from  the  west,  as  it  should  be.  Taking  the  results  for 
the  two  zones  separately,  it  is  seen  that  in  each  the  difference 
between  winter  and  summer  is  very  nearly  the  same,  but  that 
for  the  average  of  the  whole  year  the  direction  is  from  a 
westerly  point  33°  24'  farther  north  in  the  pressures  above  760 
mm.  than  in  those  below  760  mm.  This  is  in  accordance  with 
theory;  for  the  low  pressures  are  more  in  the  interior  of  the  great 
cyclone,  where  the  gyrations  above,  at  least  in  the  lower  cloud- 
region,  may  not  only  have  little  anti-cyclonic  motion,  but  even 
some  cyclonic  motion,  and  hence  the  directions  should  be  from 
a  point  farther  south  than  in  the  outer  border,  in  the  zone  of 


STATIONARY  CYCLONES.  321 

high  pressures,  where  the  great  anti-cyclone  above  may  extend 
over  all  Europe. 

Of  course,  the  individual  observations  are  affected  by  the 
varying  pressures  of  every  transient  cyclone  passing  along,  but 
in  the  averages  of  great  numbers  of  observations  the  effects  of 
these  are  mostly  eliminated,  and  we  have  left  mostly  that  of 
the  great  stationary  cyclone  only. 

212.  The  conditions  of  an  ordinary  stationary  cyclone  are 
found  in  summer  on  every  island  in  the  ocean ;  for  since  the 
annual  range  of  temperature  on  land  is  much  greater  than  that 
of  the  ocean,  the  mean  annual  temperature  on  land  and  sea 
being  very  nearly  the  same,  the  island  in  summer,  especially  in 
high  latitudes  where  the  annual  temperature  changes  are  great, 
becomes  very  much  warmer  than  the  surrounding  ocean.  And 
this  is  not  merely  an  incipient  condition,  such  as  is  required 
generally  to  originate  a  cyclone  when  the  other  conditions  of 
proper  vertical  temperature  gradient  and  hygrometric  state  are 
present,  but  it  is  continuous,  especially  during  the  day,  and 
keeps  up  the  vertical  and  cyclonic  circulations  independently 
of  the  other  conditions.  Of  course  this  condition  is  confined 
to  the  island,  and  so  there  is  no  progressive  motion.  The 
cyclonic  action,  however,  is  of  no  great  violence,  for  the  tem- 
perature differences  and  gradients  are  mostly  in  the  lower  strata 
of  the  atmosphere,  and  in  the  great  body  of  air  in  the  upper 
strata  they  are  small.  Their  power,  therefore,  to  give  rise  to  a 
vertical,  and  so  to  a  cyclonic,  circulation  is  small,  but  this  is 
very  much  increased  where  the  interior  of  the  island  consists, 
of  highlands,  as  has  been  explained  in  §  132  in  the  case  of 
monsoons. 

Australia  furnishes  such  conditions  in  some  measure,  but 
the  island  comprises  too  great  a  range  of  latitude  for  a  perfect 
cyclone,  which  requires  that  the  area  shall  be  of  smaller  extent ; 
and  besides  it  is  too  near  the  equator  for  the  influence  of  the 
earth's  rotation  to  be  considerable,  especially  on  its  equatorial 
side.  The  effect,  therefore,  arising  from  the  temperature  con- 
ditions here  has  been  treated  as  monsoonic  and  not  cyclonic^ 


322  CYCLONES. 

though  some  allowance  has  been  made  for  the  deflecting  force 
of  the  earth's  rotation  upon  the  directions  of  the  winds. 

During  the  summer  season  the  great  continents  of  Europe, 
Asia  and  America  are  heated  up  considerably  above  the  sur- 
rounding regions,  which  give  rise  to  vertical  circulations,  inward 
below  and  outward  above,  giving  rise  to  the  summer  monsoons, 
and  causing  considerable  barometric  depressions  in  the  interior, 
especially  in  Asia,  but  the  areas  are  of  too  great  extent  and 
comprise  too  great  a  range  of  latitude  for  much  cyclonic  effect 
to  be  produced,  and  the  lower  pressures  in  the  interior  are  to  be 
attributed  almost  entirely  to  the  differences  of  temperature,  and 
very  little,  if  any,  to  cyclonic  gyrations.  The  influence,  how- 
ever, of  the  deflecting  force  of  the  earth's  rotation  upon  the 
directions  of  the  monsoon  winds  is  no  doubt  considerable. 


COLD  WAVES  AND   NORTHERS. 

213.  It  frequently  happens  in.  the  United  States  during  the 
winter  season  that  there  are  large  and  progressive  areas  of  in- 
tense cold  which  originate  mostly  in  the  extreme  Northwest 
and  progress  easterly  and  southeasterly,  frequently  as  far  as  the 
Atlantic  Ocean.  On  account  of  the  great  contrast  between 
the  temperature  of  this  air  and  that  which  it  encounters,  its 
easterly  progression  causes  very  great  and  sudden  changes  of 
temperature,  and  hence  it  is  called  a  "  cold  wave."  Those 
down  in  Texas  are  generally  called  "  Northers." 

These  cold  waves  have  been  investigated  by  Lieut.  Wood- 
ruff5?  of  the  Signal  Service,  for  the  years  1881-84.  He  finds 
that  they  occur  in  winter  only,  and  more  in  January  than  in  any 
other  month  ;  that  86  per  cent  originate  east  of  the  Rocky 
Mountains  and  14  per  cent  come  across  these  mountains,  and 
that  by  far  the  greatest  number  travel  across  the  country  from 
Helena,  Montana,  to  the  Atlantic  in  32  to  40  hours.  He  gives 
instances  of  temperature  changes  of  40°  to  50°  F.  in  24  hours. 

These  cold  waves  are  closely  connected  with,  and  form  a 
part  of,  the  cyclones  which  pass  over  the  United  States,  and 
an  explanation  of  them  has  been  already  partially  given  in  the 


COLD    WAVES  AND  NORTHERS.  323 

•explanation  of  the  trough-phenomena  and  weather  sequences 
in  the  passage  of  a  cyclone  over  any  given  place  (§  193).  The 
whole  cold  area,  however,  is  not  due  entirely  to  the  whirling  of 
colder  air  from  higher  to  lower  latitudes  on  the  west  side  of  the 
cyclone,  but  also,  in  a  great  measure,  to  the  increased  terrestrial 
radiation  in  winter  through  the  clear  air  on  the  clearing-up  side 
of  the  cyclone,  especially  on  the  high  plateaus  east  of  the 
Rocky  Mountains.  The  easterly  progressive  motion  of  this 
<:old  air  west  of  the  Mississippi  River  is  increased  by  the  easterly 
slope  of  this  plateau,  upon  the  same  principles  that  winter  mon- 
soons and  land  winds  are,  in  the  case  of  high  and  sloping  pla- 
teaus in  the  interior  of  a  country ;  so  that  the  cold  stratum  is 
actually  forced  under  a  cyclone  a  little  beyond  the  centre,  but 
cannot  advance  faster  than  the  cyclone  which  it  follows,  and 
upon  which  it  in  a  great  measure  depends  for  its  origination 
and  continuance. 

214.  That  a  cold  wave  is  simply  the  rear  part  of  a  cyclone 
with  the  degree  of  cold  mpre  than  usually  intensified  by  certain 
favorable  circumstances,  is  evident  from  the  fact  that  we  have 
preceding  and  accompanying  it  the  same  sequences  of  tempera- 
ture, wind,  and  pressure  which  are  observed  in  high  latitudes  in 
the  passage  of  cyclones  in  the  winter  season,  when  the  trough- 
phenomena  are  developed.  There  are  first  southeasterly  and 
southerly  winds,  moist  air,  increasing  cloudiness  and  rain,  and 
low  pressure ;  then  follow  a  sudden  change  of  the  wind  to  the 
north  or  northwest,  a  rapid  increase  of  pressure,  and  a  lower- 
ing of  the  temperature.  Lieut.  Woodruff  says:57 — 

"  In  studies  upon  the  origin  and  movements  of  areas  of  high  and  low 
barometer  it  has  been  shown  generally  that  they  move  almost  invariably 
across  the  United  States  from  west  to  east.  The  determination  of  the 
movement  of  the  area  of  low  barometer  largely  determines  the  move- 
ment of  the  following  high.  Now  most  of  the  areas  of  low  barometer  are 
formed  in  the  region  east  of  the  Rocky  Mountains,  and  as  these  areas 
move  eastwardly  the  high  moves  in,  and  we  have  accompanying  a  cold 
wave  of  more  or  less  intensity.  Even  if  the  low  area  pursue  an  abnormal 
track  the  circulation  of  the  winds  about  the  high  and  low  is  such  as  to 
produce  almost  invariably  a  decided  fall  in  temperature,  if  the  low  be 
•eastward  of  the  high." 


324  CYCLONES. 

In  the  general  easterly  progression  of  the  atmosphere,  and' 
by  the  unusually  high  pressure  in  the  Northwest  of  the  United 
States  at  the  time  of  cold  waves,  it  is  possible  that  a  thin 
stratum  of  the  lower  very  cold  air  travels  entirely  across  to  the 
Eastern  States;  and  this,  when  the  temperature  of  the  earth's 
surface  is  very  low,  and  especially  when  it  is  covered  with  snow, 
which  prevents  the  heat  of  the  earth  below  from  coming  through 
readily  to  warm  up  the  air  above,  continues  very  cold  all  the 
way.  Under  these  conditions  the  flow  of  air  from  the  north 
or  northwest  may  extend  to  a  long  distance  before  its  tempera- 
ture is  much  changed.  The  coldest  winter  weather  is  experi- 
enced in  the  middle  and  southern  latitudes  of  the  United  States, 
when  the  whole  country  is  covered  with  snow,  and  there  is  an 
area  of  very  high  barometer  and  low  temperature  in  the  north- 
ern part,  or  in  British  America.  But  whether  the  air  in  the 
rear  of  a  cyclone  comes  from  the  extreme  Northwest,  or  directly 
down  from  higher  latitudes,  we  are  not  safe  in  predicting  a 
cold  wave  in  the  middle  and  southern  latitudes,  from  the 
occurrence  of  an  area  of  very  high  barometer  and  low  tempera- 
ture in  the  North  or  Northwest,  if  the  intervening  surface  of 
the  earth  is  warm  and  uncovered  with  snow,  since  the  stratum 
of  cold  air  becomes  warmed  up  before  it  travels  very  far. 

The  cold  waves  are  said  to  not  occur  in  summer,  but  even 
in  this  season  there  are  similar  changes,  but  of  course  not  so 
marked,  which  give  rise  to  agreeable  changes  from  very  warm 
to  cooler  weather,  and  which  may  be  called  "  Cool  Waves." 

As  most  of  the  areas  of  low  barometer,  or,  in  other  words, 
cyclones,  originate  in  the  region  east  of  the  Rocky  Mountains, 
so  the  cold  waves,  which  are  their  rear  parts,  we  have  seen, 
originate  there  also,  and  both  progress  across  to  the  Atlantic 
Ocean  together. 

Again  Lieut.  Woodruff  says  : 

"It  is  observed  that  some  of  the  severest  'northers'  in  Texas  occur 
when  an  area  of  low  barometer  appears  near  the  coast,  the  winds  at  Gal- 
veston  and  Indianola  are  easterly,  and  the  temperature  high;  the  'low' 
moves  northeasterly,  the  winds  back  to  northerly  and  northwesterly,  and 
the  temperature  falls  more  or  less  rapidly,  according  to  the  rapidity- 


COLD    WAVES  AND  NORTHERS.  325 

with  which  the  low  moves  off.     If  the  storm  have  considerable  energy, 
the  '  norther'  is  severe  and  sudden." 

Here  again  the  cold  wave  or  norther  is  the  west  side  of  a 
cyclone,  and  the  intensity  of  the  former  seems  to  depend  upon 
that  of  the  latter.  The  northers  of  Texas  are  noted  for  the 
greatness  and  suddenness  of  the  changes  from  high  to  low  tem- 
peratures. The  cyclone  here  which  gives  rise  to  the  northers 
being  near  the  coast  of  the  Gulf  of  Mexico,  and  the  contrast 
in  winter  between  the  temperature  of  the  land  and  the  Gulf 
being  very  great,  the  warm  air  of  the  Gulf  is  carried  northward 
over  the  land  on  the  east  side  of  the  cyclone,  while  the  colder 
air  of  higher  latitudes  is  brought  down  on  the  west  side,  and 
pressing  under  the  cyclone,  comes  in  contact  with,  and  rather 
meets,  the  southeasterly  much  warmer  and  moister  air  on  the 
other  side ;  and  when  this  line  of  meeting,  or  trough  of  the 
•cyclone,  passes  over  a  place,  there  is  a  great  and  sudden  change 
•of  temperature. 

215.  An  interesting  and  instructive  paper  on  the  northers 
•of  Texas  was  read  at  the  meeting  of  the  American  Association 
for  the  Advancement  of  Science  about  20  years  ago  by  Solomon 
Sias,58  who  seems  to  have  resided  in  Texas  for  some  time  and 
to  have  made  many  observations  of  them.  The  following  ex- 
tracts are  taken  from  this  paper  and  given  here  with  the  ex- 
planations and  comments  following : 

"The  wind  from  whatever  quarter  blowing,  usually  S.S.E.  or  S.W., 
either  entirely  dies  away  or  very  materially  slackens,  and  is  changed  to 
-a  cold,  piercing  north  wind.  This  is  a  norther.  .  .  .  Frequently,  we 
may  say  usually,  the  change  is  so  sudden  and  marked  that  a  person 
standing  in  the  open  air  feels  it  slap  him  with  a  chilling  roughness,  and 
almost  immediately  the  moisture  is  dried  upon  him  which  the  preceding 
warmth  had  produced.  While  riding  over  the  prairies,  uncomfortably 
warm  in  the  lightest  clothing,  I  have  repeatedly  been  struck  by  them, 
and  before  I  could  wrap  my  blanket  around  me,  been  as  uncomfortably 
cold." 

"  Sometimes,  instead  of  changing,  the  preceding  wind  dies  entirely 
^away,  and  a  dead,  oppressive,  suffocating  calm  ensues,  to  be  broken  in  a 
few  hours  by  the  wild  bursts  of  the  descending  norther." 

"They  frequently  commence  faint  as  a  summer's  zephyr,  again  bend 
the  trees  like  reeds,  and  I  have  known  the  brick  walls  of  our  Institute  to 


326  CYCLONES, 

quiver  at  the  first  striking  of  the  blast.  .  .  .  They  die  down  in  a  few- 
hours  to  a  force  of  about  two,  hold  at  this  rate  perhaps  a  day  or  so,  then, 
fade  entirely  away." 

"The  wind  in  a  norther  is  not  always  strictly  from  the  north  ;  it  fre- 
quently veers  for  a  few  hours,  to  N.E.  or  N.W.,  or  back  and  forth  be- 
tween these  points,  and  I  have  known  it  to  give  way  completely  for  an 
hour  or  two  to  a  southerly  wind.  This  veering  and  changing,  however, 
seldom  occurs  in  the  early  stages,  or  in  a  norther  of  a  high  degree." 

"  The  total  number  of  northers  in  a  year  varies  from  thirty-five  to- 
forty- eight ;  the  average  is  about  forty-two  or  forty-three.  We  are  told 
they  commence  the  last  of  September  and  end  in  May;  but  meteorolog- 
ical observations  show  they  commence  earlier  and  end  later;  in  fact,, 
there  is  no  month  in  which  they  may  not  occur." 

"The  thermometer  frequently  falls  rapidly  at  their  commencement,. 
— it  is  said,  sometimes  seventy  degrees  in  fifteen  minutes  ;  but  I  have 
never  witnessed  such  rapid  or  extreme  falls.  The  greatest  I  have  noted 
is  twenty  degrees  the  first  hour  and  fifteen  the  next,  making  thirty-five 
degrees  in  two  hours;  and  this  is  a  very  exceptional  case." 

"  Usually  the  barometer  commences  falling  from  two  to  six  days  before 
a  norther  sets  in,  and  drops  down  slowly  but  pretty  regularly  until  the 
first  stroke  of  the  norther,  when  it  rises  rapidly.  Frequently  the  fall  is 
more  rapid  just  before  the  change;  and  I  have  often  been  led  to  the  be- 
lief that  a  norther  was  close  at  hand  by  this  phenomenon,  in  the  ab- 
sence of  othej  usual  indications,  and  I  do  not  remember  ever  being  dis- 
appointed. And  the  almost  invariable  fact  that  it  rises  the  moment  one 
begins  has  sometimes  been  my  first  and  surest  evidence  that  one  is 
blowing." 

"  The  northers  may  be  divided  into  two  classes, — the  wet,  or  those 
accompanied  by  rain,  sleet,  or  snow;  and  the  dry,  in  which  the  sky  is 
clear,  or  but  partially  covered  with  clouds.  If  the  preceding  wind  has 
been  east  or  south,  we  usually  look  for  a  wet  norther ;  if  it  has  been 
directly  south,  the  sky  laden  with  clouds,  and  the  norther  does  not 
scatter  them  immediately,  it  may  be  wet;  if  the  wind  has  been  west  of 
south,  it  is  usually  a  dry  norther." 

"The  northers  are  mere  surface  winds.  When  the  wind  is  ranging 
from  three  to  five,  the  clouds,  and  even  down,  are  frequently  seen  float- 
ing in  the  opposite  direction.  The  gusts  of  wind  sometimes  seem  to 
actually  roll  along  the  ground." 

As  heralds  of  the  approach  and  attendants  during  the 
progress  of  a  norther,  Mr.  Sias  states  : 

"A  warm,  moist  wind  blows  from  some  southerly  quarter  a  few  days  ; 
the  thermometer  rises;  the  barometer  sinks  slowly,  then  rapidly;  the 


COLD    WAVES  AND  NORTHERS.  327 

wind  materially  slackens,  veers  to  the  west  or  gives  way  to  a  dead,  op- 
pressive calm ;  and  lastly,  a  peculiar  dark  cloud-like  appearance  forms 
in  the  northwestern  horizon,  slowly  rises,  and  when  in  a  few  hours  it 
reaches  an  angle  of  thirty  or  forty  degees,  the  norther  bursts  upon  us." 

"  The  attendants  are  usually  the  immediate  rise  of  the  barometer  and 
falling  of  the  thermometer ;  sometimes  a  dash  of  rain,  occasionally  the 
ozonic  smell  and  curdling  of  the  air;  almost  invariably  the  rapid  disap- 
pearance of  the  northern  cloud-like  formation;  and  frequently  so  great 
a  reduction  of  temperature  that  a  frost  or  freezing  occurs  out  of  season." 

216.  From  a  mere  reading  of  these  extracts  and  those  from 
Lieut.  Woodruff's  paper,  and  comparing  them  with  §  193,  it  is 
seen  that  in  cold  waves  and  northers  we  simply  have  the  usual 
trough-phenomena  of  cyclones  in  their  passage  over  a  place, 
where  these  phenomena  are  well  marked.  These,  we  have 
seen,  occur  mostly  in  winter,  and  in  latitudes  where  cyclones 
have  an  easterly  progressive  motion,  and  rarely  in  summer ; 
and  precisely  the  same  is  true  of  cold  waves  and  northers.  In 
all  there  are,  first,  mostly  southerly  and  southeasterly,  warm 
and  damp  winds,  accompanied  by  a  gradually  falling  barometer, 
which  toward  the  last  becomes  very  rapid.  Then  comes  the 
dividing  line  between  the  warm  southerly  and  southeasterly, 
and  the  cold  northwesterly  winds,  which,  on  account  of  the 
great  difference  of  temperature,  do  not  readily  mix,  and  so 
there  is  a  sudden  passage  from  the  one  to  the  other.  There  is, 
on  this  line,  a  very  steep  pressure  gradient  for  a  short  distance, 
which,  however,  soon  passes  over,  and  during  this  time  the 
squalls  are  often  terrific  ;  after  which  there  are,  for  several  days, 
the  usual  westerly  winds  of  the  rear  of  the  cyclone.  Some- 
times, however,  it  seems  that  there  is  not  this  very  sudden 
change,  but  the  central  dead  calm  is  observed  for  a  short  time. 
This  is,  no  doubt,  when  the  centre  of  the  cyclone  passes  over 
the  place,  and  when,  for  some  reason,  the  trough-phenomena 
are  not  so  well  developed  as  usual. 

The  northers,  like  cyclones,  mayor  may  not  be  accompanied 
by  rain,  that  is,  at  any  given  place,  though  there  is,  perhaps, 
always  more  or  less  rain  somewhere.  When  the  preceding 
winds  are  west  of  south,  as  they  are  mostly  when  the  track  of 
the  cyclone  is  on  the  north  side  and  the  place  is  on  the  south 


328  CYCLONES. 

side  of  the  cyclone  and  out  of  the  rain  area,  there  is  no  rain, 
and  the  norther  is  called  a  dry  norther.  On  the  other  hand, 
if  the  preceding  winds  are  southeasterly,  as  they  are  when  the 
central  part  or  the  northern  side  of  the  cyclone  passes  over  the 
place,  and  this  falls  within  the  rain  area,  the  norther  is  called  a 
wet  norther. 

The  norther  is  said  to  be  a  mere  surface  wind,  and  the 
clouds  above  are  frequently  seen  floating  in  the  opposite  direc- 
tion. A  stratum  of  the  cold  air  of  no  great  depth  is  naturally 
forced  under  the  warmer  and  lighter  air  on  the  southeast  side 
of  the  cyclone,  where  the  usual  cyclonic  motions,  giving  rise  to 
southerly  and  southeasterly  winds,  prevail.  Besides,  at  the 
dividing  line,  where  the  pressure  gradient  is  very  steep  for  a 
little  distance,  and  the  air  rushes  out  with  great  velocity,  there 
is  a  return  current  above  at  no  great  height. 

At  the  line  of  meeting  of  the  winds  of  nearly  opposite 
directions  and  great  contrasts  of  temperature,  the  warm  moist 
winds  are  thrown  up,  and  somewhat  over  the  stratum  of  cold 
air  which  they  meet,  and  the  cooling  of  this  moist  air,  both  by 
ascent  and  by  coming  into  contact  with  the  cold  air,  causes  the 
usual  "  dark,  cloud-like  appearance  which  forms  in  the  north- 
western horizon/'  and  which  is  usually  seen  at  some  distance, 
and  for  some  time  before  the  norther  arrives,  but  which  gen- 
erally soon  passes  by.  In  high  latitudes,  where  the  colder  air 
is  below  the  freezing-point,  the  mingling  of  the  warm  and 
moist  air  with  it  gives  rise  not  only  to  a  very  strong  wind,  but 
also  to  a  dense  snow-storm,  called  a  "  blizzard,"  *  in  which  per- 
sons who  are  caught  are  sometimes  unable  to  find  their  way 
to  a  place  of  shelter  and  protection,  and  often  perish. 

Since  cold  waves,  by  the  preceding  explanation,  depend 
upon  cyclonic  gyration  and  a  large  temperature  gradient  in  a 
north  and  south  direction,  they  should  not  only  abound  mostly 
in  winter  when  the  gradient  at  any  place  is  largest,  but  also  in 
countries  where,  at  the  same  season,  this  gradient  is  greatest. 

*  This  term  is  said  to  have  had  its  origin  amongst  the  Germans  of  Dakota, 
who  called  a  wind  of  this  sort  a  blitzartig  (lightning-like)  wind,  and  finally  a 
blitzart  simply,  which  was  changed  by  the  English  settlers  to  blizzard. 


PAMPEROS.  329 

In  the  Mississippi  valley,  between  the  warm  Gulf  of  Mexico 
.and  the  cold  regions  of  the  northern  and  northwestern  part  of 
North  America,  the  temperature  gradient  is  very  steep.  And 
as  the  changes  depend  upon  the  progressive  motions  of  the 
cyclones,  these  changes  should  be  most  sudden  where  the  pro- 
gressive motions  are  most  rapid,  as  in  the  United  States  of 
America.  Hence  here  the  cold  waves  are  most  numerous, 
«and  the  changes  of  temperature  unusually  great  and  sudden. 
This  seems  to  be  the  view  taken  of  the  matter  by  Dr.  Hinrichs, 
who  says  (Am.  Met.  Journal,  Feb.,  1888): 

"  In  winter  the  great  thermic  gradient  of  the  Mississippi  valley  is  the 
real  cause  of  the  sudden  changes  in  our  weather.  In  this  thermic  con- 
trast between  the  north  and  the  south  we  have  the  origin  of  our  blizzards 
and  cold  waves.  This  great  difference  in  temperature  makes  it  possible 
for  us  to  have  a  thunder-storm  in  winter,  followed  in  a  few  hours  by  a 
blizzard.  The  irregular  changes  of  temperature  from  day  to  day  are 
accordingly  much  greater  in  the  Mississippi  valley  than  in  Russia.  Our 
so-called  cyclonic  storms  travel  about  twice  as  fast  as  those  in  Europe 
and  Russia." 

PAMPEROS. 

217.  The  pamperos  of  South  America,  cold  southwest  winds 
from  the  Pampas,  or  plains,  are  the  same  as  the  cold  waves 
and  northers  of  North  America.  This  will  be  at  once  seen 
from  a  few  extracts  from  Dr.  David  Christison's  paper  on  the 
pamperos  of  Central  Uruguay  : 69 

"  The  barometer  fell  pretty  steadily  from  two  to  four  and  one  half 
days  before  the  storms,  the  fall  varying  from  0.18  to  0.56  of  an  inch.  In 
two  it  began  to  rise  some  hours  before  the  storm  burst,  and  it  may  pos- 
sibly have  done  so  in  all.  In  all  it  continued  to  rise  for  some  days  after 
the  pampero. 

"  The  thermometer  in  all  cases  showed  a  marked  tendency  to  rise  for 
some  days  before  the  pampero.  Unless  interrupted  by  the  occurrence 
of  rain,  thunder,  or  a  temporary  shifting  of  the  wind  to  a  cold  southern 
point,  this  rise  seemed  to  go  on  pretty  steadily,  a  few  degrees  being 
added  every  day  to  the  heat,  in  some  instances  for  more  than  a  week. 
After  the  pampero  the  fall  was  rapid,  but  the  temperature  soon  began  to 
rise  again,  particularly  with  a  change  of  wind  to  the  east.  The  coolness 
produced  by  the  pampero  is  one  of  their  most  striking  characteristics. 


33O  CYCLONES. 

and  although  it  occurs  at  all  seasons,  it  is  particularly  welcome  in  hot. 
weather.  It  happened  in  every  one  of  the  twelve  cases  under  considera- 
tion. Comparing  the  daily  maxima  before  and  after  them,  the  average 
fall  of  temperature  was  13°  F.,  the  least  being  4°,  and  the  greatest  24°. 
The  greatest  absolute  fall  was  44°  in  14  hours ;  in  another  instance  it 
was  33°  in  6  hours. 

"  Thunder  accompanied  seven,  and  immediately  preceded  two  others. 
of  the  twelve.  It  also  occurred  within  a  few  days  before  or  after  several 
of  them  ;  but  three  were  not  accompanied  with  thunder  at  all. 

"Rain  accompanied  eight,  immediately  preceded  two,  and  closely 
followed  another.  In  some  instances  it  was  very  heavy,  in  others  quite 
trifling.  There  was  also  a  good  deal  of  rain  within  a  few  days  before 
them,  and  a  small  amount  within  the  same  period  after  them.  Only  one 
was  quite  unconnected  with  rain. 

"  The  wind  before  this  class  of  pamperos  almost  invariably  blew 
moderately  or  gently  for  several  days  from  easterly  points,  perhaps  shift- 
ing to  the  N. ;  the  change  to  S.W.  sometimes  takes  place  from  the  latter 
quarter.  Any  deviation  to  other  points  seemed  to  be  quite  exceptional. 
The  change  to  S.W.  was  sometimes  preceded  by  a  calm  ;  but  in  most, 
cases  that  I  had  the  opportunity  of  watching  closely,  the  east  or  north 
wind  continued  to  blow,  although  with  diminished  force,  until  the. 
moment  when  the  pampero  supplanted  it.  For  some  time  before  this, 
however,  the  clouds  overhead  were  either  motionless,  or  moving  very 
slowly  from  the  N.W.,  more  rarely  from  the  N.  or  W. 

"  Perhaps  the  most  striking  characteristic  of  this  class  of  pamperos 
was  the  invariably  sudden  outburst  of  the  wind  at  its  full  strength  almost 
from  the  first.  Continuing  to  blow  thus  steadily  from  ten  to  thirty  min- 
utes only — in  one  case  for  an  hour — it  then  either  ceased  entirely,  or 
more  frequently  continued  with  diminished  force  for  a  certain  number 
of  hours.  The  force  of  these  short  outbursts  varied  from  that  of  a  strong 
gale  to  a  moderate  puff  of  wind,  but  was  always  sufficient  to  mark  them 
off  distinctly  from  the  preceding  or  following  wind. 

"  Sometimes  the  wind  continued  in  the  S.W.  for  only  twelve  hours, 
but  never  more  than  three  days,  before  returning  to  some  easterly  point. 
In  general  it  spent  the  greater  part  of  the  time  in  the  S.,  changing  to 
that  quarter  soon  after  the  pampero  had  blown  itself  out.  But  in  some 
cases  it  changed  several  times  between  S.W.  and  S.  before  reverting  to 
the  east." 

From  these  extracts  it  is  evident  that  the  sequence  of  phe- 
nomena preceding  and  attending  pamperos  are  the  same  as  in 
the  case  of  cold  waves  and  northers,  except  that  in  the  direc- 
tions of  the  winds,  on  account  of  their  being  in  the  opposite 


THE  MISTRAL   AND    THE  BORA.  331 

hemisphere,  we  must  put  N.  for  S.  and  S.  for  N.  There  is  first,, 
for  several  days,  the  gradual  falling  of  the  barometer  and  in- 
crease of  temperature  with  damp  winds  from  E.  to  N. ;  then, 
sometimes  a  short  calm,  but  mostly  a  sudden  change  of  the 
wind  to  S.W.,  which  is  the  pampero  proper.  This  at  first  is 
generally  very  strong,  and  then  more  moderate,  and  is  accom- 
panied by  a  rapid  lowering  of  the  temperature  and  increase  of 
barometric  pressure.  But  the  principal  characteristic,  as  in. 
cold  waves  and  northers,  is  "  the  invariably  sudden  outburst 
of  the  wind  at  its  full  strength,  almost  at  the  first."  They  were 
usually  preceded  by  several  days  of  rain  with  thunder,  as  the 
trough  of  a  cyclone  is,  and  also  followed  by  some  rain. 


THE   MISTRAL  AND  THE   BORA. 

218.  Along  the  whole  northern  coast  of  the  Mediterranean* 
in  winter,  unusually  cold  northerly  winds  frequently  prevail  for 
several  days,  called  in  the  Rhone  valley  and  the  Gulf  of  Lyons 
the  Mistral,  in  the  Adriatic  a  Bora,  and  in  the  Grecian  Archi- 
pelago a  Tramontane  negra,  or  Black  Norther.  These  winds 
are  always  connected  with,  and  form  part  of,  a  cyclone,  and 
are  the  same  as  the  northers  of  Texas.  They  prevail  when- 
ever there  is  a  cyclone  so  situated  in  the  Mediterranean  that 
the  currents  of  the  northwestern  side  of  the  cyclone  bring  the 
comparatively  very  cold  air  from  higher  latitudes  down  to  the 
Mediterranean  coast ;  for  along  this  coast  in  winter  there  is  a 
contrast  between  the  land  and  sea  temperature  similar  to  that 
between  Texas  and  the  Gulf  of  Mexico.  But  the  mistral  and 
the  bora  are  strengthened  by  the  prevailing  belt  of  high 
pressure  north  of  them  in  winter,  extending  from  the  Atlantic 
over  the  Spanish  peninsula,  France  and  Austria,  on  toward  the 
interior  of  Asia,  Woeikoff  s  "  Great  Axis  of  the  Continent,"  " 
which  gives  rise  to  a  prevalence  of  northerly  winds  at  all  times 
along  the  northern  coast  of  the  Mediterranean  during  the 
winter.  These  winds,  as  those  of  the  cold  waves  and  northers 
of  North  America,  are  also  strengthened  by  any  area  of  high- 
pressure  existing  from  any  cause  at  the  time  to  the  north  orr 


332  CYCLONES. 

northwest   of  them,  and  which   may  be  nearly  or  quite  inde- 
pendent of  the  cyclone. 

These  winds  are  especially  cold  after  there  has  been  high 
pressure  and  very  clear  and  cold  weather  over  the  mountain- 
ous regions  to  the  north,  when  the  air,  very  cold  from  radia- 
tion from  the  mountain  sides,  runs  down  and  settles  in  the 
valleys.  When  all  the  conditions  favorable  to  the  norther  are 
at  hand,  this  very  cold  air  is  drawn  down  to  the  Mediterranean 
-coast,  and  even  on  to  much  lower  latitudes.  "  In  the  eastern 
part  of  the  Mediterranean,  the  northerly  winds  reach  to  the 
African  coast,  continue  over  Egypt  and  the  Nubian  desert, 
.and  have  even  been  felt  on  the  Nile  as  far  south  as  8°  or  9° 

:N."18 

Since  these  winds  are  always  connected  with  a  cyclone,  they 
last  generally  only  a  few  days,  until  after  the  cyclone,  in  its 
progressive  motion,  has  passed  away.  There  is  here,  however, 
usually  no  sudden  transition  from  very  warm  and  moist  to  very 
cold  and  dry  air,  as  in  the  case  of  cold  waves  and  northers, 
^since  the  direction  of  progressive  motion  is  toward  the 
N.N.E.,  very  nearly  in  the  direction  of  the  trough  of  the 
cyclone,  or  line  separating  the  warm  winds  on  the  south- 
easterly side  from  the  cold  winds  of  the  northwesterly  side. 

THE  FOEHN  AND  THE  CHINOOKS. 

219.  It  sometimes  happens  that  near  the  base  of  a  high 
mountain  range  for  several  days  there  are  unusually  warm  and 
dry  winds  coming  from  the  direction  of  the  mountain.  These 
are  noted  winds  on  both  sides  of  the  Alps,  especially  on  the 
north  side,  and  are  called  there  and  elsewhere  the  Foehn  ;  but 
in  the  northwest  part  of  North  America,  east  of  the  Rocky 
Mountains,  Chinooks.  Although  the  true  explanation  of  these 
winds  was  given  by  Espy,  yet  it  is  only  somewhat  recently, 
since  the  full  explanation  of  them  by  Dr.  Hann,  that  they 
have  been  generally  understood.  They  are  connected  with, 
-and  are  a  part  of,  cyclones,  just  as  the  northers  of  Texas  and 
:the  Mediterranean. 


THE  FOEHN  AND    THE   CHI  NOOKS.  333; 

The  effects  of  several  permanent  foehns,  depending  upon 
the  general  motions  of  the  atmosphere  over  mountain  ranges, 
have  already  been  referred  to  and  explained  (§  128).  In  the 
same  manner  temporary  foehns  are  produced  wherever  there  is 
a  cyclone  so  situated  as  to  draw  a  current  of  air  over  a  high 
mountain  range,  and  the  effect  is  particularly  marked  where 
this  air  is  drawn  from  warmer  latitudes  and  is  very  moist. 
For  then  the  air  is  warm  at  the  beginning  of  the  ascent,  and 
being  very  damp,  it  is  seen  from  Table  III  that  after  having 
ascended  to  only  a  very  moderate  altitude,  its  rate  of  cooling 
with  increase  of  altitude  in  its  ascent  is  comparatively  slow,  so 
that  on  arriving  at  the  top  it  still  has  a  high  temperature  for 
the  altitude.  In  its  descent,  now,  it  becomes  warmed  up  i°  C. 
for  each  100  meters,  and  so  on  arriving  at  the  base  of  the 
mountain  on  the  other  side,  as  it  is  drawn  in  toward  and 
around  the  centre  of  the  cyclone,  it  has  a  much  warmer  tem- 
perature than  that  of  the  surrounding  air,  and  than  that  which 
usually  prevails  at  the  season.  And  having  lost  most  of  its 
vapor  in  ascending  to  the  top  of  the  mountain,  it  of  course 
becomes  a  very  dry  wind  after  descending  to  the  base  of  the 
mountain  on  the  other  side,  down  perhaps  to  about  the  same 
level  as  that  from  which  it  started. 

Dr.  Hann  has  shown  that  the  foehn  of  Switzerland  occurs 
when  there  is  a  large  cyclone  of  considerable  intensity  with  its 
central  depression  in  the  direction  of  the  British  Isles,  or 
beyond  in  the  Atlantic  Ocean,  and  high  barometer  S.E.  of 
the  Alps,  and  the  foehn  on  the  south  side  of  the  Alps,  when 
the  reverse  is  the  case ;  that  is,  when  the  low  pressure  is  in 
the  Mediterranean  S.E.  of  the  Alps  and  high  pressure  in  the 
direction  of  the  British  Isles.  He  has  given  a  graphic  repre- 
sentation of  each,  which  may  be  regarded  as  typical  cases — the 
one  of  the  great  foehn  of  January  31,  1885,  south  foehn  in 
Switzerland,  and  the  other  of  the  foehn  of  October  5,  1884, 
north  foehn,  on  the  south  side  of  the  Alps.60  In  the  case  of 
the  south  foehn,  the  wind  is  drawn  across  the  Alps  in  the 
southeast  part  of  the  great  cyclone,  and  in  the  other  from  the 
north  side  by  the  slight  cyclonic  action  in  this  case  of  a  cyclone 


:334  CYCLONES. 

in  the  Mediterranean,  but  mostly  forced  across  by  the  very  high 
pressure  in  the  direction  of  the  British  Isles.  The  foehn  on 
the  north  side  is  generally  the  most  marked,  because  of  the 
permanent  cyclone  in  the  winter  season  in  the  north  Atlantic ; 
for  the  depression  of  an  ordinary  progressive  cyclone,  added  to 
that  of  the  southeastern  side  of  the  permanent  one,  frequently 
causes  a  great  depression  on  the  eastern  coast  of  Europ.e  or  the 
contiguous  part  of  the  Atlantic. 

220.  The  chinook  winds  of  Virginia  City,  of  our  North- 
west Territory,  have  been  investigated  by  Professor  Harring- 
ton61 from  the  bulletins  of  Weather  Reports  of  the  Signal 
Service  for  several  years.  He  shows  that  they  are  of  the  same 
character  as  the  foehns  of  Switzerland  and  other  places,  and 
•defines  them  to  be  "  warm,  dry,  westerly  or  northerly  winds 
-occurring  on  the  eastern  slopes  of  the  mountains  of  the  North- 
west, beginning  at  any  hour  of  the  day,  and  continuing  from  a 
few  hours  to  several  days"  Again  he  says:  "  The  chinooks 
occur  when  a  cyclone  is  passing  to  the  north  of  the  place  of  obser- 
vation" This  condition  is  necessary  in  order  that  the  westerly 
wind  of  the  southwesterly  part  of  the  cyclone  may  draw  the 
;air  across  the  main  divide  of  the  Rocky  Mountains  to  the  place 
of  observation  on  the  east  side. 

The  chinooks  are  felt,  more  or  less,  along  the  whole  eastern 
^side  of  the  Rocky  Mountain  range,  from  the  southern  part  of 
Colorado  at  least  as  far  north  as  Peace  River,  in  British 
America,  and  to  a  considerable  distance  east  of  the  range,  the 
area  in  which  they  are  most  marked  including  most  of  Wyo- 
ming, much  of  Montana,  and  some  of  Dakota,  and  they  are 
perceptible  as  far  east  as  Bismarck,  about  500  miles  east  of  the 
main  divide.  "A  marked  effect  of  the  chinooks  is  the  ameli- 
oration of  the  winter  temperature  caused  by  them.  On  the 
arrival  of  the  chinooks  the  winter  appears  to  yield.  The  air 
becomes  mild,  and  to  the  residents  of  this  naturally  dry  region 
appears  balmy  and  spring-like."  61 

To  the  effect  of  the  frequent  occurrence  of  chinooks  in  this 
region,  but  perhaps  mostly  to  the  more  permanent  foehn  effect 
of  the  westerly  winds  due  to  the  general  motions  of  the  atmos- 


THE  FOEHN  AND    THE    CHI  NOOKS.  335 

phere,  as  explained  in  §  128,  is  due  the  general  mildness  and 
dryness  of  the  winter  in  comparison  with  the  greater  seventy 
and  dampness  experienced  farther  toward  the  east  on  the  same 
latitudes.  So  dry  are  these  warm  winds  that  they  immediately 
evaporate  the  melted  snow,  and  it  seems  to  pass  directly  and 
very  rapidly  into  vapor  without  wetting  and  softening  that 
which  is  left.  They  are  consequently  sometimes  called  "  snow- 
eaters." 

With  regard  to  the  chinooks  of  British  America,  George 
M.  Dawson62  of  Ottawa,  Canada,  says : 

"As  experienced,  the  chinook  is  a  strong  westerly  wind,  becoming 
almost  a  gale,  which  blows  from  the  direction  of  the  mountains  out  across 
the  adjacent  plains.  It  is  extremely  dry,  and,  as  compared  with  the 
winter  temperature,  warm.  Such  winds  occur  at  irregular  intervals  dur- 
ing the  winter,  and  are  also  not  infrequent  during  the  summer,  but  being 
cool  as  compared  with  the  average  summer  temperature,  are  in  conse- 
quence then  not  commonly  recognized  by  the  same  name.  When  the 
ground  is  covered  with  snow,  the  effect  of  the  winds  in  its  removal  is 
marvellous,  as  owing  to  the  extremely  desiccated  condition  of  the  air,  the 
snow  may  be  said  to  vanish  rather  than  to  melt  the  moisture  being 
licked  up  as  soon  as  it  is  produced." 

Similar  foehn-like  winds  are  experienced  in  all  parts  of  the 
world,  under  different  names,  wherever  a  current  of  air  is 
drawn  or  forced  over  a  high  mountain  range.  They  are  more 
marked  in  the  winter  season  of  high  latitudes,  because  in  this 
case  the  vertical  gradient  of  the  undisturbed  atmosphere  is 
small,  so  that  .the  temperature  of  the  air,  descending  from  a 
high  altitude  and  heated  at  the  rate  of  i°  C.  for  each  100 
meters,  is  much  higher  at  the  lower  level  than  that  of  the  sur- 
rounding air,  or  the  air  generally  over  the  region.  In  the 
summer  season  during  the  day  when  the  earth's  surface  is  very 
warm,  and  the  decrease  of  temperature  with  increase  of  alti- 
tude great,  the  foehn  effect  is  small,  and  the  conditions  may 
even  be  such  as  to  give  them  a  lower  temperature  than  that  of 
the  surface  air  generally. 


CYCLONES. 


THE   SIROCCO. 

221.  There  is  in  Italy  and  the  eastern  part  of  the  Mediter- 
ranean still  another  warm  wind  which  is  connected  with 
cyclones,  and  is  the  counterpart  of  the  Mistral  and  the  Bora — 
the  Sirocco.  It  is  a  very  warm,  and  generally  damp,  south  and 
southeast  wind  on  the  eastern  side  of  a  cyclone,  with  its  centre 
westward  of  the  place  of  observation.  The  very  warm  and  dry 
air  from  the  Sahara  and  the  northern  coast  of  Africa  is  whirled 
around  toward  the  northeast  and  north,  and  in  passing  over  the 
sea  it  becomes  a  very  damp  as  well  as  warm  wind,  and  as  such 
mostly  it  is  experienced  in  Sicily,  Italy,  and  the  eastern  parts 
generally  of  the  Mediterranean  and  the  adjacent  coasts. 
Although  the  temperature  never  rises  above  95°  F.,  yet  on 
account  of  the  great  dampness  these  winds  are  very  oppressive, 
and  seem  to  be  of  a  higher  temperature.  This  is  due  to  local 
circumstances,  to  the  existence  of  the  highly  heated  Sahara 
from  which  warm  air  is  drawn,  which  in  its  passage  over  the 
sea  becomes  nearly  saturated  with  vapor  ;  but  the  same  in  some 
measure  is  observed  in  nearly  all  parts  of  the  world  on  the 
eastern  sides  of  cyclones,  where  much  warmer  and  damper 
winds  than  usual  prevail.  Like  all  phenomena  of  this  kind 
connected  with  and  dependent  upon  cyclones,  they  continue 
only  a  few  days,  until  the  cyclone  has  passed  away.  The  dust 
raised  from  the  Sahara  and  carried  northward  by  the  sirocco 
often  falls  over  the  countries  north  of  the  Mediterranean  as 
"  blood  rain"  or  as  "  red  snow,"  the  moisture  and  the  sand  fall- 
ing together  in  the  rain  or  snow. 

As  in  the  case  of  the  Mistral  and  Bora,  there  is  generally 
no  sudden  transition  from  very  warm  and  moist  air  to  very 
cold  and  dry  air,  as  in  the  case  of  the  northers  of  Texas, 
since  the  direction  of  the  storm's  path  here  is  nearly  that  of 
the  trough  of  the  cyclone,  which  separates  the  winds  of  the 
two  characters.  There  is,  however,  always  the  same  marked 
contrast  between  the  two  sides  of  the  storm,  and  the  storm's 
path  may  sometimes  have  such  a  direction  as  to  give  a  con- 
siderable change  of  air  in  the  passage  of  the  storm. 


CYCLONES'   WITH  A    COLD    CENTRE.  337 

Dr.  Harm60  has  given  a  graphic  representation  of  the  great 
Sirocco  storm  of  the  25th  of  February,  1879,  m  t*16  Adriatic 
Sea,  and  of  its  path,  which  lay  over  the  northwestern  part  of 
Italy,  and  extended  in  a  direction  N.N.E. 


CYCLONES  WITH  A  COLD  CENTRE. 

222.  If  for  any  reason  the  central  part  of  any  given  portion 
of  the  atmosphere  of  a  somewhat  circular  form  is  maintained 
in  any  way  at  a  lower  temperature  than  the  surrounding  parts, 
and  the  temperature  gradient  on  all  sides  is  somewhat  sym- 
metrical, we  have  approximately  the  conditions  which  give  rise 
to  a  cyclone.  In  this  case  it  is  readily  seen  that  there  must  be 
a  vertical  circulation  as  in  the  ordinary  cyclone,  but  that  it  is 
reversed,  out  from  the  centre  below,  and  in  toward  the  centre 
above,  with  a  gradual  settling  down  of  the  air  in  the  interior 
to  supply  the  outward  current  beneath.  This  vertical  circula- 
tion, as  in  the  case  of  the  ordinary  cyclone,  gives  rise  to  a 
cyclonic  motion  in  the  interior  and  an  anti-cyclonic  in  the  ex- 
terior part  of  the  air  under  consideration,  but  in  this  case  the 
gyratory  velocity  is  greatest  above  and  is  less  at  lower  altitudes, 
diminishing  down  to  the  earth's  surface,  where  it  is  least.  In 
the  anti-cyclonic  part  the  reverse  takes  place,  the  gyratory 
velocity  being  least  above  and  greatest  down  near  the  earth's 
surface.  The  distance  from  the  centre  at  which  the  gyratory 
velocity  vanishes  and  changes  sign,  is  greatest  above  and  grad- 
ually becomes  less,  with  decrease  of  altitude  down  to  the  sur- 
face, where  it  is  nearest  the  centre.  Consequently,  contrary  to 
what  takes  place  in  an  ordinary  cyclone,  the  upper  part  of  the 
air,  taken  over  the  whole  area,  is  mostly  cyclonic,  especially  if 
the  friction  at  the  earth's  surface  is  but  little,  and  there  is  con- 
siderable gyratory  velocity  below  in  the  cyclonic  part ;  for,. 
whatever  this  is,  there  is  always  a  certain  difference  between 
the  gyratory  velocities  above  and  below,  greater  or  less  accord- 
ing to  the  amount  of  temperature  gradient  between  the  central 
and  exterior  parts.  If  the  atmosphere  were  in  the  unstable 
state  for  dry  air,  and  for  any  reason  it  should  receive  a  down- 


338  CYCLONES. 

ward  motion  over  a  given  area,  either  from  a  lower  temperature 
or  for  any  other  reason,  then  this  motion  would  continue,  and 
the  central  area  would  continue  to  be  colder  as  long  as  this 
unstable  state  continued,  and  during  this  time  the  vertical  cir- 
culation would  give  rise  to  and  maintain  a  cyclone  with  a  cold 
centre,  which  would  be  a  progressive  one.  But  for  reasons 
given  in  §  162,  we  have  reason  to  think  the  atmosphere  is 
never  reduced  to  this  state,  except  through  a  stratum  of  incon- 
siderable depth  next  the  earth's  surface.  Hence  we  have  no 
progressive  cyclones  with  a  cold  centre. 

The  cases  in  nature  which  give  even  rough  approximations 
to  these  conditions  are  few,  and  these  are  such  as  to  give  rise 
to  stationary  cyclones  only.  An  island,  such  as  Iceland,  in 
winter,  when  the  air  over  the  whole  island,  and  especially  the 
interior  part,  is  much  colder  than  that  of  the  surrounding  ocean, 
furnishes  approximate  conditions  which  must  give  rise  to  con- 
siderable cyclonic  action  of  this  sort,  though  it  is  all  included 
in  the  very  much  larger  ordinary  and  stationary  cyclone  of  the 
North  Atlantic  in  the  winter  season. 

223.  The  conditions  of  a  cyclone  with  a  cold  centre  which 
are  the  most  nearly  perfect  are  those  furnished  by  each  hemi- 
sphere of  the  globe,  as  divided  by  the  equator,  in  which  the 
pole  is  the  cold  centre  and  the  temperature  gradient  from  the 
pole  toward  the  equator  is  somewhat  symmetrical  in  all  direc- 
tions from  the  centre.  It  is  true,  the  deflecting  force  of  the 
earth's  rotation  is  greatest  at  the  centre  and  decreases  with 
increase  of  distance  from  the  centre,  and  vanishes  at  the  equa- 
tor, and  the  curvature  of  the  surface  makes  the  conditions  vary 
considerably  from  those  of  a  small  portion  of  the  earth's  sur- 
face, but  still  the  general  results  are  the  same,  and  all  the  ex- 
planations given  with  regard  to  the  vertical  circulation  and  the 
east  and  west  gyratory  motions  in  the  case  of  the  general  mo- 
tions of  the  earth  are  applicable  to  the  effects  of  cyclonic  con- 
ditions of  this  sort  over  a  small  area  of  the  earth's  surface. 
The  easterly  motions  in  the  higher  latitudes  and  the  westerly 
ones  in  the  lower  latitudes,  in  the  one  case,  correspond  to  the 
cyclonic  in  the  interior  and  the  anti-cyclonic  in  the  exterior 


Cr 'CLONES    WITH  A    COLD   CENTRE.  339 

part,  and  the  belt  of  high  pressure  near  the  tropics  to  that  of 
high  pressure  in  the  case  of  any  cyclone  with  a  cold  centre. 

Looking  at  the  general  circulation  of  the  two  hemispheres 
of  the  globe  as  two  cyclones  of  this  sort,  we  see  in  another 
light  the  cause  of  the  annual  shifting  of  the  equatorial  and 
tropical  calm-belts  north  and  south,  and  why  they  are  a  little 
•nearer  the  north  than  the  south  pole.  The  tendency  of  the 
two  cyclones  is  to  expand  over  a  greater  area,  and  the  more  so 
the  greater  the  internal  energy  upon  which  their  actions  de- 
pend and  the  less  the  amount  of  friction  at  the  earth's  surface. 
As  the  outer  limit  of  each  is  common  and  the  one  tends  to 
encroach  on  the  other,  during  the  winter  of  the  northern  hemi- 
sphere, when  the  temperature  gradient  between  the  equator 
and  the  pole,  and  consequently  the  energy  of  the  cyclone,  is 
greatest,  while  at  the  same  time  that  of  the  southern  cyclone 
is  least,  the  northern  cyclone  encroaches  a  little  on  the  territory 
of  the  southern  one,  and  consequently  becomes  larger,  while 
the  other  becomes  smaller.  Hence  at  this  season  all  these 
calm-belts  have  a  position  a  little  farther  south  than  their  mean 
position.  During  the  summer  of  the  northern  hemisphere,  on 
the  contrary,  the  energy  of  the  northern  cyclone  is  diminished 
and  that  of  the  southern  increased,  and  consequently  the  re- 
verse takes  place,  and  the  calm-belts  now  have  a  position  a 
little  north  of  their  mean  position. 

The  less,  also,  the  frictional  resistances  to  the  gyratory  mo- 
tions of  a  cyclone,  the  greater  is  its  tendency  to  spread  and 
encroach  upon  the  territory  of  an  opposing  one,  and  hence  the 
southern  cyclone,  being  mostly  on  an  ocean  surface,  is  one  of 
much  greater  violence  with  the  same  amount  of  energy,  and 
the  depression  at  the  south  pole  is  much  greater  than  that  at 
the  north  pole,  and  the  tendency  is  to  occupy  a  little  more 
territory  than  its  opposing  less  violent  cyclone,  and  so  the  mean 
position  of  all  the  calm-belts  is  a  little  farther  from  the  south 
than  the  north  pole. 

224.  The  centre  of  a  cyclone  with  a  cold  centre  may,  or 
may  not,  have  a  minimum  pressure,  according  to  circumstances. 
-A  certain  amount  of  temperature  gradient,  and  of  pressure  gra- 


340  CYCLONES. 

dient  which  is  independent  of  the  gyratory  motion,  as  explained! 
in  §72  in  the  case  of  the  general  circulation  of  the  atmosphere, 
is  necessary  to  overcome  the  friction  in  the  lower  strata  and  to 
keep  up  the  vertical  circulation,  upon  which  the  cyclonic  de- 
pends;  and  the  pressure  gradient,  which  depends  upon  the 
temperature  gradient  and  is  independent  of  the  gyrations,  may 
be  such  that  the  increase  of  pressure  in  the  central  part  due  to 
this  cause  may  be  greater  than  the  decrease  of  pressure  arising 
from  the  cyclonic  gyrations,  especially  where  surface  friction  is 
great.  For  instance,  in  the  southern  hemispherical  cyclone, 
where  this  friction  is  comparatively  small,  the  cyclonic  gyra- 
tions are  comparatively  large,  and  the  effect  is  to  diminish  the 
pressure  there  more  than  it  is  increased  by  the  colder  and 
heavier  air  there.  And  this  is  also  in  some  measure  the  case 
in  the  northern  hemispherical  cyclone  ;  but  with  still  a  little 
more  of  land  surface,  and  with  still  greater  mountain  ranges, 
the  resistance  to  the  gyratory  motion  might  be  such  that  the 
decrease  of  pressure  at  the  pole  from  this  cause  would  not  be 
equal  to  its  increase  from  the  lower  temperature  and  greater 
density  of  the  air. 

Each  of  the  great  continents  of  Europe,  Asia  and  of  North 
America  furnish,  in  winter,  only  very  roughly  the  conditions  of 
a  stationary  cyclone  with  a  cold  centre,  as  they  do  in  summer 
those  of  an  ordinary  cyclone,  both  because  the  areas  are  too 
large  and  irregular,  and  also  because  the  deflecting  forces  are 
very  different  on  the  polar  and  equatorial  sides,  and  conse- 
quently not  symmetrical  in  all  directions.  The  surfaces  also 
are  very  uneven,  and  consequently  the  resistances  to  gyratory 
motion  great.  There  is,  however,  some  motion  of  this  sort,  no 
doubt,  but  it  is  not  sufficient  to  reduce  the  pressure  in  the 
central  part  as  much  as  it  is  increased  by  the  greater  coldness 
and  density  of  the  air  in  winter,  for  the  effect  of  this  is  very 
great,  and  so  there  is  a  maximum  pressure  in  the  interior  of 
these  continents  during  the  winter.  The  whole  effect  of  the 
unequal  distribution  of  temperature,  therefore,  has  been  treated 
in  Chapter  V,  and  regarded  as  a  winter  monsoon,  some  allow- 


CYCLONES    WITH  A    COLD   CENTRE.  341 

ance,  however,  being  made  for  the  deflecting  force  of  the  earth's 
rotation  upon  the  directions  of  the  monsoon  winds. 

225.  Regarding  the  general  motions  of  each  hemisphere  as 
a  cyclone,  then  all  ordinary  cyclones  become  secondaries,  and 
their  effects  upon  the  isobars  and  the  general  motions  of  the 
atmosphere  become  similar  to  those  of  the  secondaries  of  ordi- 
nary cyclones,  as  stated  in  §  208  and  represented  in  Fig.  13. 
If  the  depression  of  the  cyclone  is  considerable,  so  that  its 
pressure  gradient  is  greater  than  that  of  the  gradient  between 
the  equator  and  the  pole  where  the  cyclone  exists,  then  the 
cyclone  gives  rise  to  another  minimum,  just  as  in  the  case  of 
the  great  stationary  winter  cyclone  of  the  North  Atlantic,  as 
represented  by  the  right-hand  secondary  minimum  in  Fig.  13; 
.and  the  winds  gyrate  around  this  centre,  but  with  a  velocity 
much  greater  on  the  equatorial  than  on  the  polar  side,  in  the 
middle  and  higher  latitudes,  and  with  a  correspondingly  steeper 
gradient.  In  fact,  we  have  here  the  resultant  of  two  motions 
in  nearly  the  same  direction,  as  explained  in  §  202,  and  it  be- 
comes the  dangerous  side  of  the  storm.  In  the  northern  hemi- 
sphere the  general  gradients  between  the  pole  and  the  equator 
at  all  times  are  so  small  that  any  cyclone  of  only  a  very  mod- 
erate barometric  depression  gives  a  minimum,  but  in  the  south- 
ern hemisphere,  on  the  middle  latitudes,  as  in  the  region  of 
Cape  Horn,  where  the  general  hemispherical  gradients  are  very 
steep,  unless  the  cyclone  has  a  considerable  barometric  depres- 
sion of  its  own,  it  does  not  give  a  minimum,  but  simply  causes 
a  derangement  in  the  general  isobars  extending  east  and  west 
around  the  globe,  making  them  closer  on  the  equatorial  side, 
and  the  isobars  on  the  other  side  do  not  inclose  a  minimum, 
but  are  open,  as  represented  in  the  left-hand  secondary  in  Fig. 
13.  However,  with  a  little  greater  cyclonic  depression,  there 
is  a  minimum  even  here,  as  represented  by  the  right-hand  sec- 
ondary in  Fig.  13. 

It  is  readily  seen,  therefore,  that  the  minimum  pressure  in 
an  ordinary  cyclone,  as  observed  and  laid  down  on  synoptic 
charts,  being  the  resultant  of  two  separate  effects,  is  not  the 
place  of  the  true  centre,  especially  in  the  southern  hemisphere, 


342  CYCLONES. 

where  the  general  gradient  is  steep.  In  fact,  without  a  very 
marked  cyclonic  depression,  the  cyclone  centre  would  be  inde- 
terminate, since  there  is  no  minimum  of  pressure,  or  isobars, 
inclosing  an  area  of  lower  pressure.  In  tracing  the  paths  of 
cyclone  centres,  therefore,  unless  there  is  a  marked  cyclonic 
depression,  there  is  always  considerable  error  from  not  taking 
these  considerations  into  account,  and  the  error  in  the  middle 
latitudes  of  the  southern  hemisphere  would  generally  be  very 
great. 

226,  The  great  permanent  cyclone  of  the  North  Atlantic 
in  winter  may  be  regarded  as  a  secondary  cyclone  with  refer- 
ence to  the  great  hemispherical  cyclone  in  which  it  is  situated,, 
and  as  the  ring  of  high  pressure  of  the  secondary  on  the  equa- 
torial side  falls  somewhat  upon  that  of  the  primary,  that  isr 
upon  the  tropical  belt  of  high  pressure  around  the  globe,  the 
effect  is  similar  to  that  represented  in  Fig.  13,  in  which  the  re- 
sultant, where  the  two  rings  fall  together,  is  a  pressure  consid- 
erably higher  than  elsewhere  in  the  ring  of  high  pressure  of  the 
primary.     This  is  the  explanation  in  part  of  the  area  of  unusu- 
ally high   pressure    in    the   Atlantic    between   Spain   and   the 
United    States.     The  other  part  arises  from  the  gyration   of 
air  around  this  region  resulting   from   the  deflections  of  the 
coasts  and  mountain  ranges,  as  explained  in  §  123.     The  de- 
flecting force  arising   from   the   earth's  rotation   being  on  all 
sides  to  the  right,  and  so  in  toward  the  centre  of  this  region, 
causes  a  little  accumulation   of  atmosphere  and   increase  of 
pressure. 

AREAS   OF   HIGH    BAROMETRIC   PRESSURE. 

227.  If  only  a  single  regular  cyclone,  without   any  other 
abnormal  disturbances,  existed    in    any  part    of  the  globe,  in 
which  the  atmosphere  in  its  normal  condition  had  a  uniform 
barometric    pressure   at   all   places,  we   have   seen,  §    174,  that 
there  must  necessarily  be  a  ring  of  barometric  pressure  around 
the  central  part  of  the  area  of  low  barometer,  a  little  above  the 
normal  mean  pressure.     But  it  has  been  shown  that  the  press- 
ure of  the  atmosphere,  undisturbed  by  transient  and  progress- 


AREAS  OF  HIGH  BAROMETRIC  PRESSURE.  343 

ive  cyclones,  is  not  of  uniform  pressure  at  all  places  on  the 
earth's  surface,  but  is  made  to  vary  in  different  latitudes  by  the 
general  motions  of  the  atmosphere,  and  both  in  latitude  and 
longitude  by  the  stationary  cyclones,  and  unequal  distributions 
of  temperature  between  land  and  water,  both  in  winter  and 
summer,  giving  rise  to  monsoons,  if  not  regular  and  stationary 
cyclones.  If,  therefore,  the  inequalities  of  pressure  of  regular 
cyclones  are  superimposed  upon  all  these  other  irregularities,  a 
chart  of  the  resultant  pressures  does  not  give  regular  circular 
isobars,  and  indicate  a  regular  ring  of  high  pressure  around  an 
area  of  low  pressure,  but  the  former  are  very  much  distorted, 
and  the  latter  is  broken  up  into  areas  of  higher  and  lower  press- 
ure. The  duration  of  the  area  of  high  pressure  depends  upon 
that  of  the  cyclone,  and  generally  has  an  easterly  progressive 
motion,  somewhat  as  that  of  the  cyclone,  but  not  necessarily 
the  same,  since  it  depends  upon  many  other  irregularities  upon 
which  it  may  be  superimposed. 

But  two  or  more  progressive  cyclones  may  interfere  with  and 
overlap  one  another,  and  then  the  irregularities  thus  produced, 
together  with  other  more  permanent  irregularities,  may  make 
the  barometric  pressure  very  irregular  and  cause  great  distor- 
tions in  the  isobars  of  the  charts.  Across  the  United  States 
there  is  generally  a  pretty  regular  series  of  cyclones  passing 
from  west  to  east,  at  intervals  of  a  few  days,  of  which  the  part 
of  the  ring  of  high  barometer  on  the  west  side  of  the  one 
which  precedes,  falls  somewhat  upon  that  of  the  east  side  of 
the  one  which  follows,  causing  a  sort  of  ridge  of  high  pressure 
between  them  ;  and  if  this  is  still  interfered  with  by  other  ir- 
regularities, as  it  usually  is,  it  may  be  an  area  of  high  barome- 
ter of  almost  any  form. 

In  forty-four  cases  of  ridges  or  areas  of  high  barometer 
with  an  area  of  low  barometer  between,  passing  over  the 
United  States,  Loomis63  found  the  average  distance  from  the 
centre  of  low  barometer  to  that  of  the  areas  of  high  barometer 
preceding  and  following  to  be  about  1000  miles,  and  the  aver- 
age height  of  the  barometer  about  30.35  inches,  the,  normal 
height  being  about  30  inches.  This  indicates  that  the  average 


344  CYCLONES. 

height  of  the  rings  of  high  barometer  was  about  0.2  inch  above 
the  normal  height,  supposing  that  the  highest  parts  of  each  did 
not  in  general  fall  exactly  together. 

228,  The  areas  of  greatest  high  pressure  do  not  generally 
depend  directly  upon  cyclones,  but  only  indirectly,  and  di- 
rectly upon  low  temperature.  On  the  clearing-up  side  of  a 
cyclone  which  has  passed  ov^r  any  region,  the  air  is  clear  and 
the  terrestrial  radiation  into  space  great,  so  that  the  air  be- 
comes unusually  cold  and  dense,  and  consequently  the  baromet- 
ric pressure  greater  than  at  surrounding  places  where  the  air  is 
warmer.  Thus  on  the  morning  of  the  thirteenth  of  February, 
1888,  according  to  the  Signal  Service  Charts,  in  the  northwest- 
ern part  of  the  United  States,  the  barometric  pressure  was  be- 
low 30  inches,  the  lowest  29.6  inches,  with  partially  cloudy 
weather,  and  temperature  little  below  freezing.  By  the  next 
morning  the  low  pressure  and  cloudy  area  had  passed  off  to- 
ward the  east,  fair  and  clear  weather  prevailed,  the  tempera- 
ture over  that  region  had  fallen  about  30°  F.,  and  the  maximum 
barometric  pressure  in  Dakota  was  30.9  inches.  This  increase 
of  pressure  was  evidently  due  mostly  to  the  lowering  of  the 
temperature  by  radiation  into  space  through  the  now  clear 
atmosphere.  By  the  morning  of  the  I5th  the  region  of  highest 
pressure,  now  31.0  inches,  had  moved  eastward  to  Lake  Supe- 
rior, the  weather  being  still  very  clear  and  cold.  After  this  it 
still  moved  farther  eastward  but  rapidly  subsided. 

The  principal  cause  of  the  large  areas  of  very  high  barom- 
eter which  frequently  occur  in  the  higher  latitudes  in  winter 
is  undoubtedly  found  in  the  clearness  of  the  atmosphere  over 
these  areas  and  the  intense  coldness  produced  by  the  radiation 
of  heat  at  a  time  when  little  is  received  from  solar  radiation. 
The  density  and  pressure  of  the  air  are  much  increased  from 
this  cause,  and  the  areas  are  too  large  and  irregular  for  this 
temperature  disturbance  to  give  rise  to  a  cyclone  with  a  cold 
centre,  by  the  gyrations  of  which  this  pressure  would  be  dimin- 
ished in  the  central  part,  as  it  is  in  the  great  hemispherical  cy- 
clones, especially  that  of  the  southern  hemisphere.  If  there 
were  no  gyrations  around  the  poles  of  the  earth,  the  polar  re- 


AREAS  OF  HIGH  BAROMETRIC  PRESSURE. 


345 


gions,  instead  of  being  areas  of  low  pressure,  as  they  are,  would 
be  areas  of  very  high  pressure. 

As  there  is  a  gradual  settling  down  of  the  air  in  the  regions 
of  unusually  high  pressure,  they  are  clear  areas,  and  since  the 
<lry  atmosphere  has  comparatively  little  radiating  power,  the 
cooling  takes  place  mostly  at  the  earth's  surface,  the  contigu- 
ous stratum  being  cooled  mostly  from  contact  with  the  earth's 
surface,  while  the  air  at  some  distance  above  is  becoming 
warmed  from  gradually  descending  and  coming  under  greater 
pressure,  an  effect  which  is  not  felt  near  the  earth's  surface, 
since  the  descending  air  does  not  reach  it  but  is  deflected  lat- 
erally and  the  air  near  the  surface  remains  under  the  same 
pressure.  Hence  the  cooling  is  so  much  greater  below  than 
at  some  height  above  the  earth's  surface,  that  the  vertical 
temperature  gradient  after  a  continuance  for  some  time  of  high 
barometric  pressure  becomes  inverted,  and  the  temperature  is 
higher  above  than  below.  A  remarkable  instance  of  this  kind 
occurred  in  France  during  two  periods  of  January,  1880.  The 
following  table  shows  the  minimum  temperature  observed  dur- 
ing these  periods  at  the  several  places  named  :64 


DATES. 

Pare   St.  Maur, 
Paris  (altitude 
46  ro.). 

Poitiers  (alti- 
tude 117  m.). 

Clermont  (alti- 
tude 407  m.). 

Puy-de-D6me 
(altitude 
1,467  m.). 

Pic  du  Midi 
(altitude 
2,366  m.). 

4 

-    i°.4 

—  0°-4 

-  4°.o 

-3°-o 

0°.2 

5 

-    i  -5 

—o  .6 

—  6  .0 

i  .0 

0  .0 

6 

—    i  .1 

-o  .3 

-  4  .0 

—  2   .0 

-3-5 

7 

—    i  -5 

0   .0 

-   i  .4 

—  I    .0 

-3-3 

8 

-    3  -5 

-2   -3 

-  7  .0 

—  I    .0 

-   4  .0 

9 

—     2    .O 

-3  -3 

—  7  .0 

—  2    .0 

—   4.2 

10 

-    3  -4 

-4  -4 

—  7  .0 

—  2   .0 

-5-o 

ii 

-    o  .7 

—4  -2 

-  8  .0 

—  I    .O 

—   4-5 

12 

-    4  .8 

-6  .1 

—  12   .0 

—  2   .0 

—    5-2 

13 

-    7  -6 

-5  -4 

—  7  .0 

0  .0 

—    5-4 

14 

Wanting. 

-3  -2 

—  10   .0 

-6   .0 

-   4.8 

25 

—    7  -5 

-8  .1 

—  14  .0 

-7  -o 

—  10  .9 

26 

-    9  .8 

-7  -i 

—  10   .0 

-5  -o 

—   8  .0 

27 

—    9  .0 

-6  .1 

—  12    .O 

—  2   .0 

-     8    .2 

28 

-ii  -5 

-8  .0 

—  14   .O 

—  I    .0 

—    8  .2 

29 

—  II    .0 

-5  -9 

-  5  -o 

—  I  .0 

-    5  .8 

30 

-    5  -3 

-o  .4 

—  4  .0 

I    .0 

-   5  .2 

3i 

-    5  -4 

—  i  -7 

-  4  .0 

I  .0 

—    5-2 

346  CYCLONES. 

The  Puy-de-D6me  is  about  ten  kilometers  from  Clermont. 
From  this  table  it  is  seen  that  during  the  first  and  last  parts  of 
the  month  the  temperature  at  Paris,  Poitiers,  and  Clermont 
was  generally  lower  than  at  the  top  of  the  Puy-de-D6me,  and 
frequently  less  than  that  on  the  top  of  the  Pic  du  Midi. 

According  to  the  late  Professor  Plantamour : 

"  It  happens  every  year  that  the  temperature  on  St.  Bernard  at 
several  hours,  or  even  during  several  days,  of  December  is  higher  than 
at  Geneva.  But  during  December  of  1879,  this  anomaly  lasted  during  a 
longer  period  of  time  than  usual.  The  average  temperature  of  St. 
Bernard  was  8°. 4  C.  higher  than  at  Geneva.  Out  of  the  31  days  of  the 
month,  only  during  14  days  was  it  from  o°4  to  6°. 2  C.  lower  than  at 
Geneva,  while  during  the  17  days  it  exceeded  this  by  2°  to  i6°.4." 


CHAPTER  VII. 

TORNADOES. 

229.  IN  addition  to  the  more  general  atmospheric  disturb- 
ances considered  in  the  preceding  chapters,  comprising  the 
general  circulation  of  the  atmosphere,  monsoons,  and  cyclones, 
there  is  another  and  distinct  class  of  disturbances,  with  their 
attendant  phenomena  of  waterspouts,  hail,  thunder,  etc.,  which 
are  very  local  in  character,  and  occupy  at  any  one  time  only  a 
very  small  portion  of  the  earth's  surface  in  comparison  with 
that  of  a  cyclone,  but  which,  over  this  small  area,  are  generally 
characterized  by  far  greater  violence  and  destructiveness. 
These  smaller  disturbances,  though  differing  from  one  another 
in  many  respects,  are  all  somewhat  similar  in  their  general' 
character,  and  all  depend  mostly  upon  the  unstable  state  of 
the  atmosphere.  They  all  have  more  or  less  gyratory  motion, 
and  may  therefore  all  be  included  under  the  general  name  of 
Tornado,  but  in  this  more  extended  sense  of  the  term  it  does 
not  include  necessarily  the  popular  idea  of  great  violence. 

Tornadoes  differ  from  cyclones  mostly  in  their  extent. 
Both  have  vertical  and  gyratory  circulations;  but  while  a 
cyclone  may  extend  over  a  circular  area  of  one  or  two  thousand 
miles  in  diameter,  a  tornado  rarely  affects  sensibly  at  any  one 
time  such  an  area  of  one  mile  in  diameter,  and  generally  very 
much  less.  To  understand  clearly  the  distinction  between  a 
tornado  and  a  cyclone,  it  is  necessary  to  understand  the  differ- 
ence in  the  conditions  which  give  rise  to  them.  A  cyclone", 
we  have  seen,  requires,  in  addition  to  the  state  of  unstable 
equilibrium  for  saturated  air,  such  a  disturbance  in  the  general 
equality  of  temperature  over  a  considerable  area  that  there  is 
a  central  and  somewhat  circular  area  of  higher  or  lower  tem- 
perature, from  which  arises  a  vertical,  and  consequently  at. 

347 


348  TORNADOES. 

gyratory,  circulation,  and  the  initial  extent  of  the  cyclone 
depends  upon  that  of  the  initial  temperature  disturbance. 
The  tornado,  we  shall  see,  is  independent  of  any  such  tem- 
perature disturbance  which  determines  the  initial  extent  of  the 
atmospheric  disturbance,  but  simply  depends  upon  conditions 
which  give  rise  to  very  local  disturbances  merely. 


THE   CONDITIONS   OF   A   TORNADO. 

230.  The  principal  condition  of  a  tornado  is  the  unstable 
state  of  the  atmosphere,  from  which,  with  any  very  slight  dis- 
turbance, arises  a  bursting  up  of  the  air  of  the  lower  strata  of 
the  atmosphere  through  those  above,  over  one  or  more  small 
•spots,  somewhat  as  the  vapor  of  boiling  water,  which  is  gen- 
erated mostly  at  the  bottom  of  the  containing  vessel,  bursts  up 
through  the  water  above  and  comes  to  the  surface.  But  this 
initial  start  in  the  tornado  having  once  taken  place,  the  condi- 
tion of  unstable  equilibrium  tends  to  continue  the  initial 
motions  as  long  as  this  state  continues,  unless  the  whole 
system  is  broken  up  by  great  abnormal  disturbances  and 
irregularities  of  the  earth's  surface.  The  start  being  once 
made,  the  interior  part  where  the  air  ascends  is  kept  warmer 
than  the  surrounding  parts,  exactly  in  the  manner  explained  in 
the  case  of  cyclones  in  §  159,  and  illustrated  in  the  table  of  that 
section,  and  while  the  unstable  state  and  this  warmer  central 
part  continue,  a  vertical  circulation  is  maintained,  the  air  ascend- 
ing in  the  interior,  flowing  out  in  all  directions  above  and  in 
from  all  directions  below  to  supply  the  ascending  current,  just 
as  in  the  case  of  a  cyclone  ;  but  in  this  latter  the  vertical  cir- 
culation is  of  great  extent  horizontally  in  comparison  with  its 
height,  while  in  the  tornado  the  reverse  is  the  case,  the  vertical 
>extent  being  generally  much  greater  than  the  horizontal. 

The  vertical  circulation  is  the  initial  stage  in  the  formation 
of  a  tornado,  and  so  the  tornado  cannot  originate  without  the 
-condition  of  unstable  equilibrium  which  gives  rise  to  a  vertical 
circulation.  It  is  not  necessary,  however,  that  this  state  shall 
extend  from  the  bottom  to  the  top  of  the  atmosphere,  and 


THE   COXDITIOXS  OF  A    TORNADO.  349' 

such  a  state,  perhaps,  never  exists ;  but  if  it  does,  rapidly 
ascending  air  continues  to  become  warmer  than  the  surround- 
ing air  at  the  same  level  up  to  the  highest  strata,  and  the 
difference  of  temperature  there  is  the  greatest.  This  condition 
would,  of  course,  give  the  strongest  ascending  current  and 
vertical  circulation.  The  ascending  current  in  this  case  has  a 
maximum  velocity  at  some  very  high  altitude,  where  the 
pressure  is  the  same  as  in  the  surrounding  air  at  the  same 
altitude,  the  pressure  below  this  level  being  less  than  that  of 
the  surrounding  air  at  the  same  level,  on  account  of  its  greater 
temperature  and  less  density.  Above  this  level  the  pressure  is 
greater  than  in  the  surrounding  air,  on  account  of  the  heaping 
up  of  the  atmosphere,  the  kinetic  energy  of  the  ascending 
current  being  gradually  changed  to  the  potential  energy  of 
increased  pressure.  But  this  heaping  up  of  the  atmosphere  and 
increase  of  pressure  causes  a  lateral  deflection  of  the  ascending 
currents  in  all  directions  in  the  upper  strata  of  the  atmosphere. 
If  the  unstable  state  does  not  extend  to,  a  very  high  alti- 
tude, the  difference  of  temperature  between  the  ascending  and 
the  surrounding  air  increases  up  to  this  level,,  and  then  begins 
to  decrease,  until  at  some  higher  altitude  it  vanishes,  and  then 
above  this  it  becomes  colder  than  in  the  surrounding  air.  The 
level  at  which  the  difference  of  temperature  between  the  as- 
cending and  surrounding  air  vanishes  is  an  isobaric  as  well  as 
an  isothermic  surface.  The  velocity  of  the  ascending  current 
is  increased  up  to  this  level ;  above  this  the  air  is  colder  and 
the  pressure  greater  than  in  the  surrounding  air  at  the  same 
level,  but  this  does  not  necessarily  extend  to  the  top  of  the 
atmosphere.  Below  that  level  the  temperature  is  greater  and 
the  pressure  less  in  the  ascending  current  than  in  the  surround- 
ing air  at  the  same  level,  and  the  greater  the  difference  of 
pressure,  the  greater  the  force  by  which  the  kinetic  energy  is 
generated,  and  the  whole  kinetic  energy  at  any  level  is  the 
equivalent  of  the  sum  of  the  differences  of  the  forces  from  some 
lower  stratum  of  the  earth's  surface  where  the  difference  of 
pressure  and  the  ascending  current  begins.  Above  this  level 
the  difference  of  temperature  and  of  pressure  is  reversed,  the-. 


'35°  TORNADOES. 

temperature  of  the  ascending  current  being  the  less  and  the 
pressure  the  greater,  and  the  greater  the  difference  of  pressure 
the  greater  the  rate  at  which  the  kinetic  energy  of  the  ascend- 
ing current  is  diminished.  The  condition  of  stability  of  the 
air  here  may  be  such  that  the  temperature  is  diminished  and 
the  pressure  increased  at  such  a  rate  that  the  ascending  veloc- 
ity and  kinetic  energy  are  brought  to  naught  before  the  top  of 
the  atmosphere  is  reached,  the  increase  of  pressure  being  suffi- 
cient to  counteract  the  ascending  velocity  before  the  top  or  a 
very  high  altitude  is  reached.  In  this  case  the  increase  of 
pressure  above  deflects  the  air  off  laterally  in  all  directions  up 
.as  high  as  the  ascending  current  reaches,  and  the  vertical  cir- 
culation extends  up  to  that  altitude  only  as  a  direct  effect  of 
the  conditions ;  but  air  of  a  higher  altitude  may  be  brought 
into  the  circulation  by  friction. 

In  what  precedes,  a  vertical  circulation  merely  is  considered, 
•and  not  the  modifying  effects  of  a  gyratory  circulation,  which 
depress,  as  will  be  seen,  the  isothermic  and  isobaric  surfaces  in 
the  interior  of  the  gyrating  portion  of  air;  so  that  in  this  case 
the  relative  temperatures  and  pressures  on  the  same  levels 
become  different. 

Again,  the  air  may  be  in  the  unstable  state  in  the  middle 
strata,  and  in  the  stable  state  both  above  and  below.  It  also 
•frequently  happens  that  the  unstable  state  exists  above,  but 
near  the  earth's  surface  the  stable  state.  This  is  especially  the 
•case  where  the  air  is  not  completely  saturated.  For  in  this 
case  the  unstable  state  near  the  earth's  surface  requires  a  de- 
crease of  temperature  with  increase  of  elevation  in  the  sur- 
rounding undisturbed  air  at  a  rate  greater  than  i°  C.  for  each 
100  meters,  which  is  rarely  found,  at  least  to  any  considerable 
altitude.  In  such  a  case  the  vertical  circulation  does  not  in- 
clude the  stable  strata  near  the  earth's  surface,  except  as  they 
may  be  acted  upon  by  means  of  friction. 

From  what  precedes,  therefore,  the  conditions  of  vertical 
•circulation,  and  consequently  of  a  tornado,  does  not  require 
that  the  unstable  state  shall  extend  to  all  strata  of  the  atmos- 
phere from  the  earth's  surface  up  to  the  top. 


THE   CONDITIONS  OF  A    TORNADO.  35 l 

231.  But  in  order  that  the  vertical  circulation  may  give 
rise  to  a  gyratory  circulation  and  to  much  violence  in  a  tornado, 
another  condition  is  necessary,  namely,  an  initial  gyratory 
motion  of  the  air  around  the  central  point  where  the  first  as- 
cent of  air  takes  place  and  toward  which  the  air  from  all  sides 
is  drawn.  This  may  be  illustrated  by  means  of  the  behavior 
•of  water  which  is  allowed  to  run  out  of  a  basin  through  a  hole 
in  the  bottom.  If  the  wrater  is  entirely  at  rest  with  reference 
to  the  basin,  it  flows  directly  in  from  all  sides  toward  and  out 
at  the  hole  without  assuming  any  gyratory  motion  ;  but  if  the 
water  is  not  entirely  quiet,  if  there  is  only  the  least  perceptible 
•disturbance,  it  is  liable  to  run,  in  the  one  direction  or  the  other, 
into  very  rapid  gyrations  near  the  centre.  The  direction  of 
the  gyration,  from  right  to  left  or  the  contrary,  depends  upon 
the  predominance  of  the  gyrations  in  the  mass  generally  in  the 
•one  direction  or  the  other,  and  does  not  require  that  the  whole 
mass  shall  have  an  initial  gyration  in  one  way.  The  case  of  the 
tornado  is  similar ;  but  instead  of  running  dowrn,  the  air  of  the 
lower  strata  runs  up  through  the  strata  above,  where  the  first 
ascent  takes  place,  and  flows  away  there  in  all  directions.  And 
if  there  is  no  initial  gyratory  motion  of  the  air,  it  runs  directly 
toward  the  centre  from  all  sides,  up  in  the  central  part  and  out 
above,  and  thus  a  vertical  circulation  is  inaugurated  and  main- 
tained, but  there  is  no  gyratory  motion  or  much  violence. 
But  if  there  are  initial  gyrations  of  the  air,  however  slight,  at  a 
distance  from  the  centre,  the  air  as  it  approaches  the  centre 
below  runs  into  a  gyration  around  that  centre,  and  the  direc- 
tion of  the  gyration  is  determined  upon  the  same  principle  as 
in  the  case  of  the  water  in  the  basin.  It  is  not  necessary  that 
the  initial  motion  of  the  air  shall  be  that  of  an  absolute  gyra- 
tion around  this  centre  as  a  fixed  point,  but  only  that  there 
shall  be  a  whirl  in  the  atmosphere  around  some  point  at  no 
very  great  distance,  such  as  to  cause  a  relative  gyratory  motion 
around  this  centre,  just  as  every  part  of  the  atmosphere,  except 
at  the  equator,  has  a  gyratory  motion  relative  to  any  assumed 
point,  in  consequence  of  the  rotation  of  the  earth  on  its  axis, 
though  an  absolute  motion  around  the  pole  only. 


352  TORNADOES. 

In  a  cyclone,  we  have  seen,  the  gyratory  motion  arises  from? 
the  absolute  motion  of  the  air  and  the  earth's  surface  around 
the  centre  of  the  cyclone,  and  not  from  initial  gyrations  which 
the  air  has  relative  to  the  earth's  surface.  In  a  tornado,  on 
account  of  the  smallness  of  its  horizontal  dimensions,  this  effect 
is  comparatively  small.  For  instance,  at  the  distance  of  1000 
meters  from  the  centre  of  a  tornado  on  the  parallel  of  45°,  the 
absolute  gyratory  velocity  relative  to  this  centre,  arising  from 
the  earth's  rotation,  is  1000  X  n  sin  45°  =  0.05  of  a  meter  per 
second,  obtaining  the  value  of  n  sin  45°  from  Table  V,  it  being 
one  half  of  2n  sin  /  for  that  latitude.  This  is  probably  less 
than  the  relative  gyratory  velocity  which  the  air  may  have  with 
reference  to  the  centre  arising  from  the  numerous  whirls  into 
which  the  air  is  being  continually  thrown  relatively  to  the 
earth's  surface  ;  but  still  it  seems  it  must  have  something  to  do 
with  determining  the  direction  of  the  gyratory  motions  in  tor- 
nadoes, since  this  is  generally,  if  not  always,  the  same  as  in 
cyclones,  and  its  effect  may  have  been  heretofore  underesti- 
mated. 

Although  the  horizontal  extent  of  the  violent  part  of  a  tor- 
nado is  small,  yet  the  air  may  be  drawn  in  slowly  from  a  much 
greater  distance  than  1000  meters,  and  so  at  this  distance  it  may 
have  sufficient  gyratory  velocity  to  determine  its  direction  ;  for, 
as  we  shall  see,  a  very  small  gyratory  motion  at  this  distance 
suffices  to  give  rise  to  a  great  gyratory  velocity  and  much  vio- 
lence near  the  centre. 

It  is  said  that  in  making  experiments  to  ascertain  whether 
the  earth's  rotation  has  any  sensible  effect  in  determining  the 
manner  of  gyrations  jn  the  flowing  of  water  through  a  hole  in 
the  bottom  of  a  large  and  shallow  basin,  it  is  impossible  to 
have  the  water  so  quiet  that  in  running  out  it  does  not  gener- 
ally run  into  a  gyration  the  one  way  or  the  other,  but  that 
there  is  no  observable  preponderance  of  the  gyrations  in  the 
direction  which  would  indicate  that  the  earth's  rotation  has 
any  sensible  influence  upon  the  direction  of  the  gyrations. 
This  is  to  be  expected  in  so  small  an  area ;  but  if  the  extent 


GYRATORY  VELOCITY  AND   ITS  EFFECT  ON  PRESSURE.    353 

of  tilt,  basin  were  as  large  as  the  base  of  a  tornado,  the  result 
would  probably  be  different. 

GYRATORY   VELOCITY   AND   ITS   EFFECT   ON   PRESSURE. 

232.  In  a  cyclone  the  base  is  so  great  in  comparison  with 
the  height,  that  the  whole  mass  of  gyrating  air  maybe  regarded 
as  a  thin  disk,  and  consequently  a  large  amount  of  the  forces 
is  spent  in  overcoming  the  frictional  resistances  at  the  earth's 
surface ;  and  the  gyratory  velocities  with  regard  to  distance 
from  the  centre  do  not  at  all  follow  the  law  which  would  hold 
in  the  case  of  no  friction.  But  in  a  tornado  the  height  is  so- 
great  in  comparison  with  the  base  that  it  may  be  regarded  as 
a  gyrating  pillar  of  air,  and  hence  the  effect  of  frictional  re- 
sistance upon  the  gyratory  velocities,  except  near  the  surface, 
is  small,  and  the  law  of  the  gyrations  at  all  altitudes  a  little 
above  the  earth's  surface  is  somewhat  the  same  as  in  the  case 
of  no  friction,  and  follows  very  nearly  the  law  of  a  free  body 
in  the  case  of  central  forces.  The  general  expression  of  this 
law  has  been  given  in  §41,  and  is  rw  =  c,  in  which  r  is  the  dis- 
tance of  the  body  from  the  centre,  and  w  is  the  absolute  gyra- 
tory velocity  of  the  body  at  that  distance  around  that  centre, 
c  being  some  constant  quantity.  Or  if,  for  simplicity,  we  neg- 
lect the  small  influence  which  the  earth's  rotation  may  have,  it 
becomes 

rv  =  r'v'  =  c, 

in  which  v  is  the  gyratory  velocity  relative  to  the  earth's  sur- 
face, and  in  which  v'  is  the  value  of  v  at  the  distance  of  r'  from 
the  centre.  It  must  be  understood  here  that  v  is  simply  the 
gyratory  component  of  a  motion  which  may  also  have  both  a 
horizontal  and  vertical  component  of  motion.  From  this  law 
it  is  seen  that  the  gyratory  component  of  velocity  v  is  inversely 
as  the  distance  r  from  the  centre,  and  hence  near  the  centre  it 
becomes  enormously  great. 

After  the  vertical  circulation  in  a  tornado  is  fully  estab- 
lished and  each  particle  of  air  has  passed  in  toward  the  centre 
and  out  several  times,  assuming  that  no  part  of  the  gyrating 


354  TORNADOES. 

column  of  air  is  changed,  although  the  initial  gyratory  veloci- 
ties at  the  same  distances  may  be  very  different  at  different 
altitudes  and  at  different  distances  from  the  centre,  yet  by  the 
mutual  action  of  the  particles  upon  one  another  by  contact  and 
by  friction,  and  from  the  tendency  of  each  one  to  follow  the 
law  of  a  free  body  with  regard  to  gyratory  velocities  at  differ- 
ent distances,  they  all  soon  have  approximately  the  same 
gyratory  velocities  at  the  same  distances  from  the  centre,  and 
nearly  follow  the  preceding  law,  which  makes  the  gyratory 
velocities  inversely  as  the  distance  ;  especially  at  a  little  distance 
above  the  earth's  surface  where  the  effect  of  friction  is  small. 
The  value  of  c,  then,  does  not  depend  upon  the  initial  value  of 
v'  at  any  assumed  distance  r',  but  upon  the  average  of  rv  for 
the  whole  mass  of  air  brought  into  circulation. 
233.  From  the  preceding  law  we  get 

r'v' 


so  that  for  any  assumed  value  of  v'  at  the  distance  r'  we  know 
the  value  of  v  corresponding  to  the  distance  r. 

The  centrifugal  force  of  the  gyratory  velocity  v  at  the  dis- 
tance r  is,  putting  v  for  w,  §  36,  since  we  assume  here  that  they 
are  sensibly  the  same, 

if  r"v" 

Fc  =  — m  =  — 5 —  m, 

by  putting  for  v  in  the  first  form  of  expression  its  value 
above  to  obtain  the  second  form. 

This  expression  may  be  obtained  directly  from  that  of  Fc 
in  §  40  by  neglecting  GO  in  comparison  with  v,  the  former,  as 
has  just  been  shown,  being  very  small  in  tornadoes  in  compari- 
son with  v. 

This  force,  which  becomes  very  great  near  the  centre  where 
r  is  small,  causes  a  depression  of  the  isobaric  surfaces  all  around 
the  centre  of  gyration,  which  becomes  very  great  near  the 
centre.  In  the  figure  following  let  the  curved  line  beaf  repre- 


'GYRATORY  VELOCITY  AND  ITS  EFFECT  ON  PRESSURE.  355 

sent  a  vertical  section  of  the  isobaric  surface  brought  down  to 
the  surface  of  the  earth  DE  at/,  and  let  ed  represent  a  vertical 
column  of  air  of  unit  base,  which  being  entirely  arbitrary,  may 
be  infinitely  small,  and  ad  a  similar  horizontal  prism  or  cylinder 
of  the  same  base  or  cross-section.  Since  the  pressure  of  a 
fluid  is  equal  in  all  directions,  in  order  that  the  air  may  be  in 
a  state  of  static  equilibrium,  we  must  have  the  horizontal 
pressure  ad  in  the  direction  of  d,  arising  from  the  centrifugal 
force  of  the  gyration,  exactly  equal  to  the  vertical  pressure  of 
*d  at  the  base  d  arising  from  the  force  of  gravity.  These 
spaces  being  supposed  to  be  very  small,  the  density  in  all  parts 
is  sensibly  the  same,  and  using  d  to  denote  this  density,  we 


Tiave  ed  X  8  and  ad  X  &  for  the  masses  respectively  of  these 
horizontal  and  vertical  air  columns.  Since  the  vertical  force  is 
equal  to  the  acceleration  of  gravity  multiplied  into  the  mass, 
the  expression  of  this  is  gd  X  ed.  And  putting  ad  X  8  for  m 
in  the  preceding  expression  of  the  centrifugal  force  Fet  we  get 
(r'W/r3)  X  ad  for  the  expression  of  the  latter  in  this  case. 
Equating  these  two  expressions,  we  get 

r'V 


as  a  condition  which  must  be  satisfied  in  determining  the  curved 
line  beaf. 


356  TORNADOES. 

Supposing  the  arc  ae,  Fig.  i,  to  be  very  small,  and  putting,. 
as  in  §  38,  e  for  the  ratio  between  the  lines  ed  and  ad,  we  get 
from  the  preceding  equation 


in  which  e  is  the  gradient  of  the  curve  between  the  points  a 
and  <?,  supposed  to  be  very  near  to  each  other. 

This  could  have  been  deduced  directly  from  the  expression 
of  eg  in  §  38  by  substituting  v  for  w,  since  the  effect  of  the 
earth's  rotation  here  being  supposed  to  be  insensible,  v  becomes 
sensibly  equal  to  wt  and  then  substituting  for  v  the  preceding 
expression  of  it.  For  it  is  very  evident  that  the  gradient  of  a 
surface  upon  which  a  body,  acted  upon  by  the  force  of  gravity 
and  a  horizontal  centrifugal  force,  must  be  the  same  as  that  of 
a  liquid  surface,  or  of  an  isobaric  surface,  where  the  liquid  is 
subject  to  the  same  forces. 

It  is  seen  from  the  preceding  expression,  since  g,  rf  ,  and  v' 
are  constants,  that  as  r3  increases,  the  gradient  e  of  the  curve 
diminishes,  and  at  an  infinite  distance  from  the  centre  C,  Fig.  I, 
it  must  vanish,  —  that  is,  the  isobaric  surface  must  become  a 
level  surface.  Also,  near  the  centre,  where  r  is  very  small,  the 
gradient  becomes  very  steep,  and  the  more  so  the  nearer  the 
centre. 

234.  If  we  let  Cx  and  Cy,  Fig.  I,  represent  the  two  rec- 
tangular co-ordinates  of  any  point  a  of  the  curve  bcaf,  then 
Cy  =  xa  is  represented  by  r  in  the  notation  above,  and  denot- 
ing the  line  Cx  =  ya,  the  depression  of  the  curve  at  the  point 
a,  by  /,  the  equation  of  the  curve  or  expression  of  /becomes* 


*  By  the  principles  of  the  differential  calculus,  if  we  suppose  the  points  a 
and  e  in  the  curve,  Fig.  I,  to  be  infinitely  near  to  each  other,  the  lines  ed  and 
tf^/are  represented  by  the  differential  expressions  —  dl  and  dr  respectively,  and 
the  equation  becomes 

—  gdl  =  r  ^v  V~3*/r. 

The  integration  of  this  gives  the  expression  of  /  above. 


GYRATORY  VELOCITY  AND  ITS  EFFECT  ON  PRESSURE.  357 

From  this  expression  it  is  seen  that  neither  one  of  /  or  r  can 
vanish  unless  the  other  becomes  infinitely  great,  and  conse- 
quently the  curve  cannot  cut  either  of  the  lines  CB  or  Cc,  in 
Fig.  i,  produced,  but  simply  approximates  to  them  and  touches 
them  at  an  infinite  distance  only,  as  a  hyperbolic  curve  does  its 
assymptotes. 

For  any  other  isobaric  surface  which,  before  being  depressed 
by  the  centrifugal  force,  corresponded  to  the  line  A'B',  either 
below  or  above  the  other,  it  is  evident  that  we  must  have  a 
similar  curve,  since  v'  is  supposed  to  be  the  same  at  all  alti- 
tudes. If  it  is  lower,  it  is  brought  down  to  the  earth's  surface 
Tepresented  by  the  line  DE,  at  a  point  f  farther  from  the 
centre  than  /",  but,  if  higher,  at  some  point  between  c  and  f. 
But  however  high  the  undisturbed  isobaric  surface  may  be,  the 
value  of  r  at  the  earth's  surface  cannot  vanish.  Also,  the  verti- 
•cal  distance  mn,  Fig.  I,  between  the  two  isobaric  surfaces,  is 
the  same  at  all  distances  from  the  centre,  and  equal  to  the 
vertical  distance  aa'  or  bb' . 

It  is  seen  from  the  preceding  expression  of  /  that  it  vanishes 
only  where  the  value  of  r  is  infinite,  whatever  the  value  of  r'v'. 
But  the  greater  v'  is  at  any  distance  r ',  and  in  the  ratio  of  its 
square,  the  greater  is  the  depression  /  at  any  given  distance  r 
from  the  centre,  until  /becomes  equal  to  the  height  Cc,  Fig.  i, 
of  the  undisturbed  isobaric  surface  AB;  and  the  value  of  r  cor- 
responding to  this  value  of  /  in  the  preceding  expression  is  the 
value  of  cfj  or  the  distance  from  the  centre,  at  which  the  iso- 
baric surface  meets  the  earth's  surface.  With  this  value  of  r 
we  get  from  the  expression  ot  v,  §  233,  where  the  value  of  v' 
at  the  distance  of  r'  is  known,  the  value  of  v  at  the  distance  cf 
from  the  centre. 

If  in  the  preceding  expression  of  /we  assume  that  at  the 
distance  of  1000  meters  from  the  centre  of  the  tornado,  as  that 
of  D  or  E,  Fig.  i,  the  gyratory  velocity  v  at  all  altitudes  is  3 
meters  per  second,  then  we  have  r'v'  =  1000  X  3  =  3000,  and 


9,000,000 
lr  = 


358  TORNADOES. 

If  we  now  suppose  that  the  height  of  any  undisturbed  isobaric 
surface  is  1000  meters,  we  then  get,  by  putting  /—  1000,  the 
value  of  r  =  21.4  m.,  for  the  distance  cf,  Fig.  i,  at  which  the 
isobaric  surface  is  brought  down  to  the  earth's  surface.  By 
assuming  any  other  value  of  /  less  than  1000  meters,  we  get  the 
value  of  r  corresponding  to  it.  For  instance,  if  the  depression,, 
as  at  a  in  the  figure,  is  ya  =  300  meters,  we  then  get  xa  or 
r  —  39  meters  nearly.  In  this  way  a  sufficient  number  of 
points  can  be  determined  to  construct  the  curve. 

At  the  distance  of  21.4  meters  from  the  centre,  by  the  pre- 
ceding relation  of  rv  =  r'v',  we  get  in  this  case 

3000 

v  =  —    -  =  140  meters  per  second 
21.4 

for  the  gyratory  velocity  at  ft  where  the  pressure  is  the  same 
as  at  b. 

In  the  same  manner  we  get  for  a  depression  of  500  meters,. 
as  at  i  in  the  figure,  r  =  30.3  m.,  and  with  this,  from  the  rela- 
tion of  rv  =  r'v'  —  3000,  we  get  v  =  99  meters  at  the  distance 
of  this  point  from  the  centre,  and  so  at/7  at  this  distance  from 
the  centre  at  the  earth's  surface,  when  the  pressure  is  the  same 
as  at  b'. 

The  curved  lines,  Fig.  I,  represent  the  form  of  the  isobaric 
surfaces  where  v'  is  taken  equal  to  5  meters  at  the  distance  of 
IOOO  meters,  and  where  the  undisturbed  isobaric  surfaces  AB 
and  A'  B'  are  taken  respectively  at  the  heights  of  1000  and  500 
meters. 

235.  The  gyratory  velocity  v  at  the  earth's  surface,  in  any 
isobaric  surface,  as  that  represented  by  baef,  Fig.  i,  is  equal  to 
the  velocity  s  acquired  by  a  free  body  in  falling  through  the 
height  BE  of  the  undisturbed  and  level  isobaric  surface,  repre- 
sented by  the  line  AB,  and  this  is  given  by  the  expression 


in  which  s  is  the  velocity  in  meters  per  second,  and  h  is  the 
height  in  meters  through  which  the  body  falls.     The  demon- 


GYRATORY  VELOCITY  AND  ITS  EFFECT  ON  PRESSURE.  359 

stration  of  this  is  too  complex  to  be  given  here,  but  it  may  be 
found  in  Recent  Advances  of  Meteorology,  p.  241.  It  is  also 
the  theoretical  velocity  with  which  a  homogeneous  fluid  issues 
from  a  fountain  at  a  level  which  is  at  the  distance  h  below  the 
level  of  the  head  of  the  fountain.  The  value  of  v,  therefore, 
at/  Fig.  i,  is  the  velocity  which  a  body  would  acquire  in  fall- 
ing through  the  space  BE\  at  f,  that  acquired  in  falling 
through  the  distance  B'E,  etc.,  no  account  being  taken  of  the 
effect  of  friction  upon  the  value  of  v. 

The  difference  of  pressure  between  /  and  /'  is  the  same  as 
that  between  i  and  f  or  that  between  b  and  b'\  and  so  the  cen- 
trifugal force  of  a  horizontal  prism  or  cylinder  ff  is  exactly 
equal  to  the  force  of  gravity  on  the  vertical  prism  or  cylinder 
if  or  bb'  of  the  same  cross-section. 

The  value  of  v  is  also  equal  to  that  acquired  by  air,  at  rest 
under  the  higher  pressure,  in  passing  horizontally  to  a  lower 
pressure,  as  for  instance  of  air  in  passing  from  E  to  /,  Fig.  i, 
or  to  velocity  arising  in  any  way  from  such  difference  of  press- 
ure, and  this,  when  the  difference  of  pressure  is  not  very  great, 
is  given  approximately  by 

P.  T    . 
s*  =  206.3  -p~AP, 

•*       J  o 

in  which,  as  before,  s  is  the  velocity  in  metres  per  second,  Pt 
is  the  standard  barometric  pressure  of  760  mm.,  P  that  where 
the  velocity  is  s,  AP  is  the  variation  of  pressure,  and  T0  and  T 
have  their  usual  significations,  being  the  absolute  temperatures 
corresponding  respectively  to  P0  and  P.  To  a  given  amount 
of  potential  energy  AP  corresponds  its  equivalent  in  kinetic 
energy,  but  the  latter,  \?m  (§  18),  is  proportional  to  the  mass 
m,  and  consequently,  for  a  given  volume  of  air,  is  as  the  den- 
sity. But  this  varies  directly  as  the  pressure  and  inversely  as 
the  absolute  temperature  T,  and  therefore  s*  must  vary  in- 
versely as  the  pressure  and  directly  as  the  absolute  tempera- 
ture, as  the  expression  above  indicates. 

By  the  preceding  expression,  if  the  pressure  P  at  /  Fig.  i, 
is  known,  and  AP  the  difference  between  /  and  £,  or  rather 


360  TORNADOES. 

between  that  at /and  at  an  infinite  distance  where  v  —  o,  the 
value  of  v  at  f  is  known,  in  case  AP  is  not  very  large.  Con- 
versely, if  v  is  known,  the  difference  of  pressure  sensibly  be- 
tween E  and  /,  or  rather  the  whole  amount  of  depression,  can 
be  computed.  At  high  altitudes  where  P  is  small  and  the  air 
rare,  it  is  seen  from  the  formula  s*  has  to  be  proportionately 
large,  where  AP  is  taken  the  same  at  all  altitudes. 

236.  On  account  of  the  great  depression  of  the  isobaric 
surfaces,  as  represented  in  Fig.  I,  the  pressure  near  the  centre 
of  tornadoes  becomes  very  much  diminished,  and  in  their  pas- 
sage over  a  place  there  is  sometimes  a  very  sudden  change  of 
pressure.  Hence,  we  see  the  reason  of  the  explosive  effects 
often  observed  during  the  passage  of  tornadoes.  Corks  fly 
from  empty  bottles,  cellar  doors  are  burst  open  against  the 
force  of  a  strong  wind  blowing  against  them  on  the  outside, 
the  walls  of  houses  are  thrown  outward  on  all  sides,  the  whole 
roof  is  suddenly  raised  up  and  blown  away,  or  the  sudden  ex- 
pansion of  air  under  copper  and  tin  covering  rips  it  up  and  it 
is  rolled  away.  And  in  case  the  walls  which  inclose  air  are  not 
tight,  but  there  are  openings  through  which  the  air  can  escape, 
towels  and  light  articles  of  clothing  which  are  carried  along 
with  the  escaping  air  have  been  found  lodged  in  them. 

"  During  the  tornado  of  Dec.  22,  1884,  in  Clarendon  County,  S.  C,  a 
lady,  perceiving  the  approach  of  a  storm,  was  in  the  act  of  closing  a  glazed 
door,  which  extended  down  to  the  floor  and  opened  on  a  piazza ;  but  be- 
fore she  could  fasten  it  the  house  was  enveloped  by  the  tempest,  the  door 
flew  open,  and  she  was  dashed  violently  against  the  balustrade  running 
around  the  piazza,  and  received  injuries  and  bruises  which  confined  her 
to  bed  for  several  weeks.  In  the  same  room  there  was  a  heavy  pine 
press,  the  door  of  which  was  locked.  This  door  was  burst  open,  torn 
from  its  hinges,  and,  in  the  language  of  the  narrator,  '  shivered  into 
kindling  splinters.'  There  was  no  damage  done  to  the  house,  or  at 
least  none  mentioned.""8 

In  the  tornado  at  St.  Cloud,  Minnesota,  a  few  years  ago, 
panels  were  torn  from  the  doors,  and  with  this  exception  the 
buildings  seem  to  have  been  untouched.  In  other  places  win- 
dow panes  were  blown  out  and  the  sash  untouched. 

The  normal  air  pressure  is  14.69  pounds  to  a  square  inch. 


GYRATORY  VELOCITY  AND   ITS  EFFECT  ON   PRESSURE.   361 

If,  therefore,  one-fourth  of  this  pressure  is  suddenly  taken  off 
from  the  outside  of  any  inclosure  containing  air  of  the  normal 
tension,  then  the  effective  explosive  force  is  3.7  pounds  to  each 
square  inch  of  the  interior  surface,  or  533  pounds  to  the  square 
foot.  And  when  we  consider  the  small  diameter  of  a  tornado 
and  its  rapid  progressive  motion,  it  is  readily  seen  how  sud- 
denly this  explosive  force  is  brought  into  play,  not  allowing 
time  for  the  gradual  escape  of  air  and  diminution  of  tension, 
even  where  the  inclosure  of  the  air  is  not  very  tight. 

237.  In  all  the  preceding  relations  between  gyratory  veloc- 
ity and  pressure  it  has  been  assumed  that  there  are  no  frictional 
resistances  between  the  air  and  the  earth's  surface,  or  between 
contiguous  portions  of  air  with  different  gyratory  velocities  at 
different  distances  from  the  centre,  and  that  these  velocities 
follow  the  law  of  rv  =  c,  as  would  be  the  case  without  friction 
where  the  air  is  drawn  in  toward,  or  recedes  from,  the  centre 
on  account  of  slight  centripetal  or  centrifugal  forces.  In  the 
case  of  friction,  however,  the  gyratory  velocities  can  only  be 
maintained  by  means  of  a  vertical  circulation  from  which  arise 
deflecting  forces  which  overcome  the  frictional  resistances  to 
the  gyrations.  In  the  case  of  friction,  therefore,  we  cannot 
have  a  strictly  gyratory  velocity,  as  we  could  if  there  were  no 
friction  to  be  overcome,  but  besides  the  gyratory  velocity  v, 
also  two  other  components  of  velocity,  the  one  the  velocity  u, 
of  radial  motion  toward  or  from  the  centre,  and  the  other  the 
velocity  x,  of  vertical  motion.  Putting,  therefore,  s  for  the 
velocity  of  the  resultant  motion,  we  have 

/  =  x*  +  «*  +  v\ 

But  in  this  case  s  is  less  than  v  in  the  preceding,  where  there  is 
the  same  difference  of  pressure  between  the  points  of  initial 
and  final  velocity,  since  in  the  case  of  friction  a  small  part  of 
the  force  due  to  difference  of  pressure  is  spent  in  overcoming 
the  frictional  resistance,  and  only  the  balance  in  producing 
kinetic  energy.  So  that  although  we  have  the  additional  com- 
ponents of  velocity  x  and  u,  yet  v  is  so  much  diminished  as  to 


362  TORNADOES. 

make  the  value  of  the  resultant  s  less  than  v  would  be  in  the 
case  of  no  resistances  with  the  same  differences  of  pressure. 

In  the  case  of  friction,  therefore,  in  which  it  is  necessary  to< 
have  a  vertical  in  connection  with  a  gyratory  circulation,  the 
motions  in  the  interior  and  lower  part  of  the  tornado  are  in 
toward  and  around  the  centre,  while  the  air  also  ascends,  but 
in  the  upper  part  it  is  around  and  from  the  centre,  the  air  still 
ascending.  But  the  gyratory  velocity  near  the  centre  of  the 
tornado  is  usually  so  great  in  comparison  with  that  of  the* 
radial  and  vertical  motions  that  x*  and  u*  do  not  add  much  to 
the  value  of  s*  in  the  preceding  expression,  and  so  s  does  not 
generally  differ  much  from  v.  The  case  is  similar  to  that  of  a 
right-angled  triangle  in  which  one  leg  is  considerably  shorter 
than  the  other  and  the  square  of  the  smaller  one  adds  but  lit- 
tle to  the  sum  of  the  squares,  and  so  the  hypothenuse  does  not 
differ  much  in  length  from  the  longer  leg. 

Since  in  the  case  of  friction  a  part  of  the  forces  arising  from 
differences  of  pressure  goes  toward  overcoming  the  frictional 
resistances,  it  is  evident  that  the  theoretical  relations  which  have1 
been  obtained  between  velocities  and  differences  of  pressure 
upon  the  hypothesis  of  no  friction,  is  not  strictly  applicable  in 
the  usual  cases  where  there  is  more  or  less  friction,  but  often 
considerable  allowances  must  be  made  for  its  effect ;  so  that 
the  velocities  corresponding  to  differences  of  pressure  are 
never  quite  so  great  as  they  would  be  in  the  case  of  no  fric- 
tion ;  just  as,  in  the  case  of  fountains,  the  water  does  not  issue 
from  the  orifice  with  that  velocity  with  which  it  would  in  case 
of  no  friction,  and  so  is  not  thrown  vertically  upward  to  the 
height  of  the  head  of  the  fountain.  The  gyratory  velocities 
also,  denoted  by  v,  in  the  case  of  friction  are  less  in  the  interior 
than  those  given  by  the  law  rv  =  c,  where  c,  depending  upon 
the  initial  gyrations  of  the  air,  is  known. 


THE   ENERGY   OF  A  TORNADO. 

238.   In  case  of  friction,  we  have  seen,  a  gyratory  circula- 
tion cannot  be  maintained  without  the  vertical,  nor  the  latter 


THE   ENERGY  OF  A    TORNADO.  36$ 

without  a  supply  of  energy  to  overcome  the  frictional  resistances, 
to  such  a  circulation.  This  is  found  in  the  supply  of  heat  which 
originates  and  maintains  the  vertical  circulation  by  inducing 
and  keeping  up  the  unstable  state  ;  for  as  long  as  this  state  is 
maintained,  the  central  part  of  the  tornado,  where  the  air 
ascends,  is  warmer  than  the  surrounding  air,  from  which  arises 
a  force  which  maintains  the  vertical  circulation.  The  latent 
heat  of  the  vapor  given  out  in  condensation  as  the  air  ascends 
plays  an  important  part,  and  is  perhaps  absolutely  essential, 
since  in  the  case  of  dry  air  the  unstable  state  could  not  be  in* 
duced  up  to  a  considerable  altitude,  and  maintained  sufficiently 
long  to  give  rise  to  a  tornado,  as  it  would  require  a  vertical 
gradient  of  temperature  decreasing  with  the  increase  of  altitude 
at  a  rate  greater  than  i°  C.  for  each  100  meters.  In  this  case 
the  heat  would  have  to  be  continually  supplied  to  the  lower 
strata  as  fast  as  it  would  be  diminished  by  the  vertical  inter- 
change between  the  lower  and  upper  strata,  in  order  to  keep 
up  the  unstable  state. 

In  the  case  of  saturated  ascending  air,  we  have  seen  that 
the  unstable  state  is  maintained  with  a  vertical  temperature 
gradient  which  is  only  about  half  as  great,  and  one  which  is. 
readily  induced  in  the  atmosphere  and  easily  maintained,  and 
so  the  supply  of  air  nearly  or  quite  saturated  for  the  ascending 
current  is  very  important,  since  the  latent  heat  furnished  be- 
comes available  energy  in  maintaining  the  interior  part  of  the 
tornado  warmer  than  the  surrounding  part  with  a  much  lower 
temperature  in  the  lower  strata,  and  a  smaller  vertical  gradient 
of  decreasing  temperature. 

Thermal  energy  is  available  in  doing  work  of  any  kind,  or 
in  producing  kinetic  energy,  only  where  there  are  differences 
of  temperature,  that  is,  temperature  gradients.  For  instance, 
if  the  whole  atmosphere  were  heated  up  equally  in  the  equa- 
torial and  the  polar  regions  to  a  very  high  temperature,  there 
would  be  no  general  circulation  of  the  atmosphere,  and  no 
expenditure  of  thermal  energy  in  producing  motion  and  kinetic 
energy  and  overcoming  the  resistances  to  motion.  In  the  case 
of  a  tornado  it  requires  not  only  a  vertical  temperature  gra- 


364  TORNADOES. 

<Iient,  but  this  must  be  such  as  to  induce  the  unstable  state. 
In  this  case  the  effective  force  in  maintaining  an  ascending 
current  and  a  vertical  circulation  depends  upon  the  difference 
of  temperature,  or  temperature  gradient,  taken  along  an  iso- 
baric  surface ;  so  that  the  greater  this  difference  of  temperature 
between  the  interior  and  ascending  air  and  the  surrounding  air, 
the  greater  is  this  force.  But  this  difference  cannot  be  main- 
tained unless  the  atmosphere  is  kept  in  the  unstable  state  for 
saturated  air  by  the  continual  supply  of  heat  to  the  lower  strata 
as  it  is  drawn  away  by  the  ascending  current.  If,  however,  the 
atmosphere  is  not  merely  unstable,  but  considerably  beyond 
the  neutral  condition,  before  the  ascending  current  and  vertical 
-circulation  set  in,  there  is  a  considerable  reserve  of  energy, 
which  suffices  to  maintain  the  motion,  until  the  unstable  state 
is  gradually  reduced  either  to  the  neutral  or  the  stable  state. 
And  this  latter  state  can  be  produced  not  only  by  the  convec- 
tion of  heat  in  the  ascending  air  currents,  but  also  by  the  sup- 
ply of  air  for  the  ascending  current  which  is  gradually  becoming 
-drier,  since  the  drier  the  air  the  greater  the  difference  of  tem- 
perature required  between  the  lower  and  the  upper  strata,  and 
for  the  lower  part,  up  to  where  the  vapor  in  the  ascending  cur- 
rent begins  to  condense,  the  gradient  of  decreasing  temperature 
has  to  be  more  than  i°  C.  for  each  100  meters.  As  there  is  no 
expenditure  of  energy  until  motion  commences,  so  the  more 
rapid  this  motion,  the  greater  the  rate  at  which  energy  is 
expended. 

239.  In  the  origination  and  first  starting  of  a  tornado,  the 
force  which  overcomes  the  inertia  of  the  air  and  causes  motion, 
is  the  difference  of  pressure  depending  upon  the  difference  of 
temperature  between  the  interior  and  exterior.  This,  in  the 
lower  strata  of  the  atmosphere,  is  a  centripetal  force,  and  as 
the  air  is  drawn  in  toward  the  centre  the  velocity  is  accelerated, 
and  where  there  is  initial  gyratory  motion,  the  body  is  at  the 
same  time  deflected  from  its  course  ;  but  the  velocity  at  any 
time  is  the  same  as  if  the  same  force  had  acted  during  the  same 
time  in  a  radial  direction  without  any  gyratory  motion  and  de- 
decting  force,  for  the  latter,  we  have  seen,  does  not  increase 


THE  ENERGY  OF  A    TORNADO.  365; 

the  kinetic  energy,  but  simply  changes  the  direction  of  motion. 
After  the  vertical  and  gyratory  circulations  are  fully  established,, 
the  whole  force  arising  from  difference  of  pressure  due  to  dif- 
ference of  temperature  goes  to  overcome  the  frictional  resist- 
ances, and  no  part  to  creating  motion  and  kinetic  energy,  and 
the  velocity  of  the  vertical  circulation  is  such  that  the  resist- 
ances are  exactly  equal  to  the  forces.  In  the  case  of  no  friction, 
no  forces  are  needed  to  maintain  ^the  circulation  after  it  is 
once  inaugurated,  and  so  no  difference  of  temperature  between 
the  interior  and  the  exterior  and  expenditure  of  heat  energy, 
but  if  there  is  such,  it  tends  to  continually  accelerate  the  verti- 
cal circulation.  The  kinetic  energy  of  the  gyratory  velocity 
has  its  exact  equivalent  in  the  potential  energy  of  the  differ- 
ence of  pressure  caused  by  the  centrifugal  force  of  the  gyra- 
tions, and  where  there  is  friction  and  a  necessity  for  a  vertical 
circulation,  there  must  be  a  difference  of  temperature  and  a 
corresponding  difference  of  pressure  arising  from  it,  to  over- 
come the  frictional  resistances  to  this  circulation. 

In  a  cyclone,  for  reasons  given  in  §  232,  the  forces  are  mostly 
spent  in  overcoming  the  resistances,  while  in  a  tornado  they 
are  spent  mostly  upon  the  inertia  of  the  air,  and  so  the  rela- 
tions between  gyratory  velocities  and  distances  from  the  centre 
are  nearly  those  given  by  the  law  of  rv  =  c,  and  between  these 
velocities  and  differences  of  pressure,  or  pressure  gradients, 
those  given  in  §  233,  determined  upon  the  principle  that  the 
difference  of  pressure  is  caused  almost  entirely  by  the  centrifu- 
gal force,  which  of  course  is  only  approximately  so  in  the  case 
of  friction,  since  a  little  force  and  difference  of  pressure,  even 
in  the  open  air  at  some  distance  above  the  earth's  surface,  is 
necessary  to  maintain  the  vertical  circulation. 

240.  In  a  vertical  circulation  arising  from  the  unstable 
state,  where  there  is  no  gyratory  motion,  the  force  which  gives 
rise  to  and  maintains  the  ascending  current  depends  upon  the 
difference  of  pressure  in  the  column  of  ascending  air  and  the 
surrounding  undisturbed  air  at  the  same  levels ;  and  if  we 
assume  that  the  force  is  spent  mostly  upon  the  inertia  of  the 
air,  and  but  little  in  overcoming  the  friction,  we  can  determine 


.•366  TORNAbOES. 

-approximately  the  velocity  of  the  ascending  current  from  the 
•differences  of  temperature  and  pressure,  where  these  are  known. 
At  the  earth's  surface  the  vertical  component  of  velocity  is 
nothing,  and  the  pressure  at  the  base  of  the  ascending  column, 
if  we  neglect  the  friction  of  the  current,  is  the  same  as  at  the 
•earth's  surface  in  the  surrounding  parts.  The  differences  of 
temperature  in  the  ascending  current  and  the  surrounding  un- 
disturbed air,  in  the  case  of  tornadoes  is  the  same  as  in  the 
case  of  cyclones  between  the  columns  A  and  C  or  C'  in  the 
table  of  §  159,  or  between  D  and  F,  or  G  and  /.  Of  course 
these  differences  depend  very  much  upon  the  assumed  vertical 
gradient  of  temperature  and  the  hygrometric  state  of  the  air, 
as  exemplified  in  the  table,  and  there  may  be  cases  in  nature 
in  which  the  temperature  differences  between  a  column  of  as- 
cending air  and  one  in  the  exterior  undisturbed  air  are  much 
^greater  than  those  in  the  table  under  the  assumed  conditions. 
The  maximum  differences,  it  is  seen,  are  about  5°  C.  Let  us 
assume  that  the  average  difference  of  temperature,  taken  with 
regard  to  mass  and  not  volume,  in  the  column  of  ascending  air 
and  one  in  the  surrounding  undisturbed  air,  up  to  the  altitude 
where  the  pressure  at  the  same  level  is  equal,  is  3°  C.,  and  that 
the  level  of  equal  pressure  is  at  the  height  where  the  barometric 
•pressure  is  equal  to  380  mm.  Supposing  the  mean  tempera- 
ture of  the  air  column  below  the  level  of  equal  pressure  to  be 
o°  C.,  then  the  difference  of  pressure  of  the  column  of  ascend- 
ing air  below  this  level  and  of  a  similar  column  in  the  sur- 
rounding undisturbed  air,  and  the  effective  potential  energy 
in  causing  kinetic  energy  at  the  height  of  the  column,  is  the 
3/273  part  of  380  mm.,  or  4.2  mm.  With  this  value  of  A  P  in 
the  last  expression  of  /  in  §235,  putting  P=  380  and  T=  T0, 
as  it  is  very  nearly  by  the  table  of  §  13,  we  get  s  =  42  m.,  nearly, 
for  the  velocity  per  second  due  to  the  difference  of  pressure 
between  the  two  columns.  Or  by  Table  VI  we  have  the  value 
•of  h  for  each  millimeter  of*  barometric  pressure  at  the  pressure 
of  380  mm.  and  at  the  temperature  of  o°  C.  equal  to  21.03  m»- 
and  so  for  4.2  mm.  equal  to  88.33  m.,  and  with  this  value  of  // 
•multiplied  into  2g=  19.61  m.,  we  get  by  the  first  form  of  the 


THE   ENERGY  OF  A    TORNADO.  367 

-expression  of  s*  in  §  235,  the  same  value  of  s  as  above  by  the 
last  form.  This  theoretical  result  is,  of  course,  considerably 
diminished  by  the  effect  of  friction,  which  is  not  taken  into  the 
account  in  the  theory. 

241.  Where  the  atmosphere  is  in  the  unstable  state  all  the 
way  up  to  the  top,  or  even  to  very  high  altitudes  only,  the 
level  at  which  the  pressures  in  the  ascending  air  and  at  the 
same  level  in  the  surrounding  undisturbed  air  are  the  same, 
where  there  is  no  depression  in  the  interior  from  gyratory 
motion,  is  very  high,  and  the  effective  force  in  causing  ascend- 
ing velocity  is  great.  But  if  the  unstable  state  of  the  atmos- 
phere does  not  extend  very  high,  as  is  undoubtedly  the  case 
often,  the  horizontal  isobaric  surface  is  not  very  high.  The 
unstable  state  may  extend  to  so  low  a  level  only,  that  the 
kinetic  energy  of  the  ascending  current  may  be  destroyed  by 
the  pressure  of  the  column  of  air  before  the  current  reaches 
the  top  of  the  atmosphere.  In  that  case  the  ascending  current 
is  deflected  off  laterally  in  all  directions  below  this  level,  and 
the  isobaric  surfaces  above  that  level  are  not  affected  directly 
•by  the  thermal  conditions,  though  they  are  all,  together  with 
those  below,  depressed  by  the  gyratory  motion  of  the  tornado  ; 
but  as  the  vertical  circulation  in  this  case  depending  upon 
differences  of  temperature  extends  only  up  to  a  certain  height, 
the  air  above  this  can  only  be  brought  into  the  gyration  by 
the  friction  between  it  and  the  gyrating  air  below,  and  an 
inverse  vertical  circulation  induced  indirectly  in  the  air  above. 
For  while  the  gyrations  are  more  rapid  below  than  above,  the 
tendency  is  to  carry  the  comparatively  little  disturbed  air 
above  out  and  around  the  centre,  and  to  draw  down  that  above 
in  the  central  part,  just  as  has  been  explained  in  the  case  of 
cyclones,  where  the  vertical  circulation  from  temperature  dis- 
turbances does  not  extend  to  the  top  of  the  atmosphere,  and 
the  interior  dry  and  clear  air  above  is  brought  down  into  the 
central  part  and  causes  the  "  eye"  of  the  cyclonic  storm.  In 
this  way,  if  the  duration  of  the  tornado  were  long  enough,  and 
the  atmosphere  were  calm,  or  had  the  same  general  motion 
above  and  below,  the  gyratory  motion  would  always  be  induced 


368  TORNADOES. 

from  bottom  to  top,  though  with  less  force  ;  but  the  time  of 
duration  being  generally  short,  and  the  general  easterly  motion 
above  being  mostly  much  greater  than  below,  tornadoes  of 
this  sort,  in  which  the  atmosphere  above  is  not  in  the  unstable 
state,  perhaps  rarely  extend  with  much  violence  to  very  high 
altitudes  in  the  atmosphere.  They  may,  notwithstanding, 
have  great  energy  and  violence,  for  the  ascending  air  escapes 
laterally  on  all  sides  above  ;  but  of  course  tornadoes,  in  general, 
are  of  the  greatest  violence,  and  the  ascending  currents  most 
rapid,  where  there  are  gyrations  and  a  rarefied  centre  extend- 
ing to  great  altitudes,  just  as  the  taller  a  flue,  the  greater  the 
draft  with  the  same  difference  of  temperature  within  and  with- 
out. 

As  in  cyclones,  as  may  be  seen  from  the  examples  in  the 
table  of  §  159,  so  in  tornadoes,  the  greatest  temperature  dif- 
ferences are  not  in  the  lower  strata  of  the  atmosphere,  but  up 
at  a  certain  altitude  above ;  or  if  the  atmosphere  is  in  the 
unstable  state  all  the  way  up,  this  difference  increases  to  the 
top.  The  conditions  may  even  be  such,  especially  if  the  air  is- 
not  nearly  saturated,  that  there  is  no  difference  of  temperature 
below  between  the  interior  and  exterior  part,  or  the  interior 
part  up  to  some  height  may  even  be  colder.  In  such  cases  the 
energy  is  mostly  at  a  considerable  altitude,  and  the  vertical 
circulation  and  the  gyrations  are  first  originated  there,  and 
gradually  communicated  to  the  strata  below  by  friction  and  by 
the  relieving  of  the  lower  strata  in  the  central  part  of  a  part  of 
the  pressure  from  the  air  above,  which  finally  gives  rise  to  an 
ascent  of  air  from  the  stratum  next  the  earth's  surface  and  a 
drawing  of  it  in  from  all  sides  at  the  surface  toward  the  centre. 

242.  If  the  gyratory  velocity  near  the  earth's  surface  in  a 
tornado  were  as  great  as  it  is  above,  there  would  not  be,  in 
general,  a  very  strong  ascending  current  in  the  interior,  for 
although  there  might  be  an  enormous  difference  of  pressure, 
yet  the  force  arising  from  this  difference  of  pressure  with  which 
the  air  would  tend  to  run  in  below  toward  the  centre  and  up  irt 
the  interior  would  be  in  a  great  measure  counteracted  by  the 
centrifugal  force  of  the  gyratory  velocity  below.  When  the 


THE  ENERGY  OF  A    TORNADO.  369 

gyratory  velocities  are  the  same  at  all  altitudes,  the  only  force 
by  which  it  flows  in  below  and  up  the  interior  is  that  due  to  dif- 
ference of  temperature  between  the  central  and  exterior  parts 
of  the  isobaric  surfaces,  by  which  the  vertical  circulation  is 
maintained.  But  even  this,  we  have  (  seen  (§  240),  under 
assumed  not  improbable  conditions,  may  give  rise  to  a  con- 
siderable ascensional  velocity.  This,  however,  is  very  greatly 
increased  in  consequence  of  the  great  frictional  resistance  to 
the  rapid  gyration  of  the  air  near  the  earth's  surface,  by 
which  the  gyratory  velocity  and  centrifugal  force  here,  which 
tend  to  prevent  the  air  from  rushing  into  the  partial  vacuum, 
are  much  diminished. 

In  the  assumed  example  of  §  234  the  difference  of  pressure 
between  the  points  f  and  £,  Fig.  I,  is  equal  to  the  pressure 
of  the  column  of  air  bE,  that  is,  equal  to  the  pressure  of  a 
column  of  air  of  1000  meters  in  height  and  of  the  average 
density  between  the  earth's  surface  and  that  altitude,  which,  in 
barometric  measure  at  an  ordinary  medium  temperature  of 
20°  C.,  as  may  be  readily  determined  by  table  VI,  is  about 
84  mm.,  since  I  mm.  of  barometric  pressure  corresponds  to- 
about  12  meters  of  altitude.  If  we  suppose  the  gyratory 
velocity  near  the  earth's  surface  beyond  f,  taking  no  account 
of  those  between  f  and  the  centre,  to  be  so  diminished  by 
friction  that  the  centrifugal  force  would  be  diminished  one 
third,  the  difference  of  barometric  pressure  between /"and  E, 
which  would  be  effective  in  causing  an  inflow  toward  the 
centre,  in  addition  to  that  considered  above  due  directly  to* 
temperature  differences,  would  be  28  mm.  This  would  give 
rise  to  a  very  great  ascensional  velocity  in  the  interior  of  the 
tornado,  not  however  near  the  earth'$  surface  but  at  some 
distance  above,  for  the  kinetic  energy  of  the  inrush  of  air  from 
all  sides  toward  the  centre  would  be  changed  to  potential 
energy  in  the  form  of  increased  pressure  in  the  central  part 
of  the  tornado  at  the  earth's  surface,  which  would  be  equal  to- 
that  at  E  if  the  whole  centrifugal  force  at  the  earth's  surface 
were  destroyed,  and  then  this  increased  pressure  would  give 
rise  again  to  kinetic  energy  in  a  rapidly  ascending  current  in. 


3/0  TORNADOES. 

the  interior,  where  the  air  is  comparatively  rare  and  the 
pressure  much  diminished  from  the  effect  of  the  gyrations 
above. 

With  the  value  of  4P=2&  mm.  or  the  corresponding 
value  of  h  taken  from  Table  VI,  either  of  the  expressions  of  j2 
in  §  235,  applied  as  in  §  240,  gives  for  a  temperature  of  20°  C., 
s  =  78.5  meters  per  second,  or  about  176  miles  per  hour.  Com- 
bined with  this  ascensional  velocity  would  be  the  gyratory  ve- 
locity of  the  ascending  air,  which  would  be  diminished  by  the 
effect  of  friction  near  the  earth's  surface,  for  the  ascending  air 
near  the  centre  would  consist  mostly  of  the  air  entering  near 
the  earth's  surface. 

243.  The  tornado  being  a  column  of  rapidly  gyrating  air,  of 
great  height  generally  in  comparison  with  its  diameter,  and 
with  the  air  very  much  rarefied  in  its  interior  from  the  effect 
of  the  rapid  gyrations  near  the  centre,  may  be  likened  to  a  tall 
flue  with  heated  and  rarefied  air  in  its  interior.  If  the  draft  of 
the  flue  is  almost  entirely  cut  off  below,  the  ascending  current 
is  feeble,  but  if  the  air  below  has  free  access,  the  velocity  of 
the  ascending  current- in  the  flue  becomes  very  great,  and  in 
proportion  to  the  difference  of  temperature  between  the  inte- 
rior and  exterior.  So  in  a  tornado,  if  the  access  of  air  were 
almost  entirely  cut  off  from  the  lower  central  part  by  the  cen- 
trifugal force  of  the  undiminished  gyratory  velocities  near  the 
earth's  surface,  the  ascending  current  in  the  interior  would  be 
of  no  great  violence,  generally  such  perhaps  as  in  the  assumed 
cases  of  §  240 ;  but  with  a  somewhat  free  access  of  air  below 
into  the  rarefied  interior,  on  account  of  a  decrease  by  friction  of 
the  gyratory  velocity  near  the  earth's  surface,  the  velocity  of 
the  uprush  of  air  in  tl^  interior  becomes  enormous.  In  this 
case  the  centrifugal  force  of  the  gyrations  in  the  open  air  a 
little  above  the  earth's  surface,  where  there  is  little  friction, 
almost  entirely  excludes  the  access  of  air  into  the  interior,  and 
serves  very  nearly  the  same  purpose  as  the  wall  of  the  flue, 
while  the  partial  destruction  of  these  gyrations  near  the  earth's 
surface  by  friction  is  similar  to  the  letting  on  the  draft  of  a  flue 
which  had  been  almost  entirely  cut  off. 


FORCE   OF   THE    WIND.  3/1 

With  an  increase  of  the  force  of  the  ascending  current,  and 
•of  kinetic  energy,  there  is  a  corresponding  increase  in  the  ex- 
penditure of  heat  energy,  for  the  more  rapid  the  current  the 
faster  is  the  condensation  of  aqueous  vapor  and  the  freeing  of 
.latent  heat,  and  the  faster  is  the  heat  of  the  lower  strata  con- 
veyed to  the  upper  ones  by  which  the  unstable  state  is  de- 
stroyed unless  heat  is  constantly  supplied  to  the  lower  strata. 
The  part  which  friction  plays  in  this  matter  is  the  facilitating 
the  application-  of  the  heat  energy  by  allowing  a  more  free  and 
rapid  vertical  circulation  and  vapor  condensation. 

FORCE    OF    THE    WIND   AND   SUPPORTING  POWER  OF  ASCEND- 
ING CURRENTS. 

244.  In  view  of  the  enormous  gyratory  and  ascensional 
velocities  in  a  tornado,  it  is  interesting  and  important  to  know 
the  destructive  force  of  the  former  and  the  supporting  power 
of  the  latter.  These  are  both  deducible  from  the  first  of  the 
expressions  of  s*  in  §  235.  According  to  this,  when  air  with  a 
velocity  of  s  impinges  against  a  barrier  at  right  angles  to  the 
•direction  of  motion,  so  that  velocity  in  this  direction  is  com- 
pletely destroyed,  or  s0  =  o,  it  gives  rise  to  a  force  which  sup- 
ports a  column  of  mercury  of  the  height  AP,  determined  by 
this  expression  where  P  and  T  are  known.  But  if  instead  of  a 
mercurial  barometer  we  use  one  of  pure  water  of  standard 
temperature,  and  denote  the  change  in  the  height  of  the  col- 
umn corresponding  to  AP  by  Ap,  we  have  Ap  =  13.596  AP,  the 
pressure  of  mercury  being  so  many  times  greater  than  water, 
and  we  then  get,  if  we  express  Ap  in  centimeters  instead  of 
millimeters, 


If  we  now  consider  the  pressure  on  a  unit  of  surface  of  one 
square  centimeter,  then,  since  by  definition  a  cubic  centimeter 
•of  pure  .water  of  standard  temperature  is  a  gram,  the  pressure 
•of  the  column  of  water  of  the  height  Ap  and  unit  base  in 


3/2  TORNADOES. 

grams,  is  dp,  and  the  pressure  upon  a  surface  of  which  the- 
area  is  A,  is  Adp,  a  gram  of  pressure  being  the  gravitational 
pressure  of  a  gram.  Putting/  for  the  pressure  of  air  in  mo- 
tion upon  a  normal  surface  area  of  A,  we  have/  =  A  dp,  and 
with  this  the  preceding  expression  gives 

P  T 


The  pressure,  therefore,  is  as  the  square  of  the  velocity  and' 
as  the  density  of  the  air,  this  latter  being  directly  as  the  press- 
ure and  inversely  as  the  absolute  temperature.  Hence,  at 
high  altitudes  where  P  is  much  less  than  P0,  the  pressure  of 
the  wind  for  the  same  velocity  is  much  less  than  near  the  sur- 
face. This  is  for  pure  and  dry  air.  For  air  with  an  average 
amount  of  moisture  in  it,  it  is  more  accurately  expressed  by 

.00659  P 

- 


The  same  formula  in  English  measures,  in  which  /  is  ex- 
pressed in  pounds  avoirdupois,  s  in  miles  per  hour,  and  A  in 
square  feet,  is 

.002698    P      2 


With  this  formula  we  get  for  the  pressure  of  wind  of  the 
velocity  of  80  miles  per  hour  upon  a  square  foot  at  the  earth's 
surface,  where  P  —  P0,  when  the  temperature  r  is  25°C.,/  = 
15.7  pounds.  At  the  altitude  where  P=  380  mm.,  with  the 
same  temperature,  the  pressure  for  the  same  velocity  would 
be  only  .half  as  much.  With  the  temperature  equal  o°  C.,  in- 
stead of  25°  C.,  the  pressure  would  be  increased  in  the  ratio  of 
10  to  ii. 

245.  The  preceding  formulae  express  the  pressure  of  the 
wind  arising  from  the  momentum  of  the  air,  or  the  change  of 
kinetic  into  the  potential  energy  of  pressure.  But  this,  as  in 
other  cases  where  friction  is  not  taken  into  account  in  the 
theory,  is  considerably  modified  by  the  effect  of  friction  ;  and 
in  this  case  the  effect  is  to  increase  the  effect,  and  not,  as  is- 


FORCE   OF   THE    WIND.  373 

usually  the  case,  to  diminish  it.  What  is  usually  called  the 
force  of  the  wind  upon  any  given  object,  as  a  plate  of  a  given 
area,  is  the  difference  of  pressure  on  the  two  sides.  On  the  one 
side  the  pressure  is  increased,  not  only  by  the  momentum  of 
the  air,  but  likewise  by  the  dragging  effect  through  friction  of 
the  air  which  passes  by,  upon  the  cone  or  pyramid  of  compara- 
tively stationary  air  in  front  of  the  plate  or  barrier.  On  the 
other  side  the  effect,  to  the  same  amount,  is  to  drag  the  air 
away  and  to  diminish  the  pressure  of  the  air.  Hence  the  theo- 
retical difference  of  pressure,  or  effective  force  of  the  wind,  is 
increased  by  equal  amounts  by  the  effect  of  friction  upon  the 
pressure  of  both  sides.  Accordingly  the  force  of  wind  deter- 
mined experimentally  is  found  to  be  a  little  greater  than  the 
theoretical  pressure  given  by  the  formulae. 

According  to  Hagen's  empirical  formula,  determined  from 
very  accurate  experiments  made  a  few  years  ago  by  means  of 
a  whirling  apparatus,  the  experimental  pressure  of  the  wind  on 
small  plates,  in  grams,  denoted  here  by/>',  is65 

p'  =  (0.00707  +  o.oooi  125^)  Fv*, 

in  which  u  is  the  periphery  and  F  the  surface  of  the  plate  in 
decimeters,  and  v  is  the  velocity  per  second  in  decimeters. 
The  average  barometric  pressure  in  the  experiments  was  758mm., 
but  no  account  seems  to  have  been  taken  of  the  temperature. 
If  we  reduce  this  expression  of/  to  English  measures  and  the 
standard  pressure,  we  get 

p'  =  (0.00289  -f  0.000140 u)  As\ 

in  which  the  notation  is  the  same  as  in  the  preceding  theoreti- 
cal expression  of/  in  English  measures. 

Supposing  Hagen's  experiments  to  have  been  made  at  a 
temperature  of  15  C.,  a  very  comfortable  working  temperature, 
and  reducing,  for  comparison,  the  preceding  theoretical  expres- 
sion of/  to  this  temperature,  we  get 

/  =  0.00255^*. 


374  TORNADOES. 

The  difference  of  these  two  expressions, 

p'  —p  —  (0.00034  -f-  o.ooo  1 4042^) 

is  the  effect  of  friction  in  increasing  the  theoretical  value  of/. 
The  plates  used  were  small,  ranging  from  about  two  to  six; 
inches  square,  and  the  velocities  in  the  experiments  were  also* 
small.  Supposing  the  average  size  of  the  plates  to  be  five 
inches  square,  the  value  of  u  become  20  inches,  equal  ta 
1. 667  feet.  With  this  value  of  u  we  get  for  the  experimental 
expression  representing  the  average  for  all  the  velocities  and 
for  all  the  plates 

p'  —  p  —  0.0005  7  A  /. 

Hence  it  is  seen  that  the  theoretical  coefficient  is  increased 
about  two-ninths  by  the  effect  of  friction. 

While  Hagen's  experimental  formula  may  very  nearly  give 
the  true  force  of  the  wind  for  the  average  of  the  plates  and 
velocities  used,  it  is  obviously  at  fault  with  regard  to  the  law  of 
variation  with  variations  of  u  and  s.  By  increasing  the  pe- 
riphery of  the  plate,  the  force,  per  unit  of  surface,  is  increased 
enormously  by  his  law,  and  the  part/'  — /,  for  very  large  plates, 
in  which  u  is  large  and  the  term  depending  upon  it,  becomes 
the  principal  term,  being  very  nearly  as  the  cubes  of  the  linear 
dimensions  of  the  plates,  or  as  uA.  For  such  a  law  there  does 
not  seem  to  be  any  reason  in  theory ;  and  more  numerous  and 
accurate  experiments,  made  with  plates  of  a  larger  range  of 
sizes,  would  undoubtedly  give  a  different  law.  It  is  improb- 
able, therefore,  that  the  formula  is  applicable  to  plates  of  a  size 
much  greater  than  those  used  in  the  experiments.  Again,  the 
formula  makes  the  part  arising  from  friction  to  be  as  the 
square  of  the  velocity,  which  is  not  in  accordance  with  either 
theory  or  experiment.  The  theory  of  the  viscosity  of  gases 
would  make  it  as  the  first  power,  and  hence  for  high  velocities 
the  force  given  by  the  formula  must  be  too  great  even  for 
small  plates. 

From  what  precedes,  it  may  be  inferred  that  about  one- 
fourth  or  one-fifth  part  must  be  added  to  the  theoretical 


FORCE   OF   THE    WIND.  375 

values  of  wind-pressures  per  square  foot  of  normal  surface  given 
by  theory,  to  obtain  the  effective  force  of  the  wind  in  moving 
objects,  this  force  being  increased  by  the  diminution  of  the 
ordinary  pressure  of  the  air  on  the  other  side  opposite  to  that 
on  which  the  wind  strikes. 

246.  The  force  with  which  the  wind  tends  to  move  a  spheri- 
cal body  is  one-half  of  that  with  which  it  tends  to  move  a  body 
with  a  normal  surface  exposed  to  the  wind  which  is  equal  to  the 
maximum  section  of  the  sphere.  The  theoretical  formula, 
therefore,  which  gives  the  pressure  p  of  the  wind  against  a 
globe,  or  the  resistance  of  the  air  to  a  globe  moving  through 
it,  is 


0.00135  — 

: - 

I  +  .004r 


in  which  the  notation  is  the  same  as  in  §  243.  But  here,  as  in 
the  case  of  wind-pressure  on  plates,  the  theoretical  pressure 
and  resistance  are  increased  by  friction  and  for  the  same 
reasons. 

From  the  two  sets  of  experiments  made  at  the  request  of 
Newton,  in  St.  Paul's  Cathedral,  at  London, — the  one  with 
several  hollow  glass  globes  of  about  5  inches  in  diameter,  let 
fall  from  an  elevation  of  220  feet,  and  the  second  one  with  sev- 
eral bladders  formed  into  spheres  about  5  inches  in  diameter, 
let  fall  from  a  height  of  272  feet,  the  weights  being  known  and 
the  times  of  descent  being  carefully  noted, — Loomis66  obtained 
from  the  first  series,  for  the  coefficient  of  resistance  to  a  globe 
5  inches  in  diameter,  the  velocity  being  in  feet  per  second, 
0.0013455,  and  from  the  second  series,  with  the  bladders, 
0.0012693,  in  ounces  Troy.  The  average  is  0.0013074.  Hence 
the  expression  of  the  resistance  to  such  a  globe,  or  of  the 
pressure  of  the  wind  against  such  a  globe,  denoted  here 
is,  in  ounces  Troy, 

/=  0.0013074^', 


376  TORNADOES. 

in  which  s  is  in  feet  per  second.  The  reduction  of  this  formula 
to  the  units  of  measure  of  §  244,  that  is,  pounds  avoirdupois, 
miles,  and  hours,  gives 

p'  =  0.00142  iAs\ 

.But  in  these  experiments,  as  in  the  case  of  Hagen's,  no  ac- 
count seems  to  have  been  taken  of  the  temperature,  and  so  we 
are  at  a  loss  to  know  what  temperature  to  use  in  the  preceding 
theoretical  expression  of  /  in  order  to  make  a  comparison  of 
the  experimental  coefficient  with  the  theoretical.  But  assum- 
ing in  this  case,  as  in  the  other,  that  the  experiments  were 
made  at  a  temperature  of  15°  C,  and  also  that  the  barometric 
pressure  was  760  mm.,  then  the  preceding  theoretical  expres- 
sion of/,  for  P  •=.  PQ  and  T  =  15°,  becomes 

/  =  0.001274^*. 
We  therefore  get 

p'  —  p  —  0.000147^*. 

Hence  the  theoretical  coefficient  is  increased  about  one-ninth 
part  by  the  effect  of  friction  in  the  case  of  spheres,  according 
to  the  preceding  experiments. 

But  Loomis  also  determined  another  coefficient  of  resist- 
ance from  the  results  of  experiments  made  by  Hutton  with  a 
whirling  machine  and  a  sphere  of  pasteboard  6f  inches  in 
diameter,  for  velocities  from  3  to  20  feet  per  second.  This  was 
found  to  be  one-fourth  greater  than  the  other.  This  great  dif- 
ference indicates  that  there  is  considerable  uncertainty  in  such 
experiments.  Adding  one-fourth  part  to  the  preceding  experi- 
mental coefficient,  we  get  in  this  case 

p'  —  0.001776^5*. 

Combining  this  with  the  previous  experimental  expression, 
giving  the  former  one  double  weight,  and  supposing  all  the  ex- 
periments  to  have  been  made  under  the  same  pressure  and 
temperature,  we  get 

p'  = 


FORCE   OF   THE    WIND.  377 

Comparing  this  with  the  preceding  theoretical  expression  re- 
duced to  the  temperature  of  15°  C.,  we  find  that,  with  this  com- 
bination of  the  results  of  the  three  series  of  experiments,  the 
effect  of  friction  increases  the  theoretical  coefficient  about  two- 
ninths,  the  same  as  in  the  case  of  the  wind  blowing  normally 
against  a  plate.  We  may,  therefore,  assume  with  considerable 
probability  that  the  theoretical  coefficient  0.002698,  in  the  case 
•of  a  plate,  is  increased  two-ninths  by  the  effect  of  friction,  and 
we  therefore  get  for  the  whole  wind  pressure  against  a  normal 
plate 

0.00330 
- 


and  for  the  pressure  against  a  sphere,  or  the  resistance  to  a 
sphere  moving  through  the  air  with  velocity  s, 

0.00165     P  A^ 
i  +  0.004T  P0 

From  the  former  of  these  the  values  of  p'  in  Table  VII  have 
been  computed  for  the  several  velocities  and  barometric  press- 
ures given  as  arguments  in  the  table,  the  temperatures  used  be- 
ing those  of  the  table  of  §  13,  corresponding  to  the  pressures  at 
different  altitudes.  These  temperatures  may  be  regarded  as 
a  sort  of  annual  means  in  the  middle  latitudes,  corresponding 
to  the  altitudes  of  the  given  pressures.  For  extreme  tem- 
peratures, deviating  considerably  from  these,  slight  corrections 
would  be  necessary  if  great  accuracy  were  required. 

According  to  this  table  and  the  formula,  the  mechanical 
force  of  the  wind  in  tornadoes,  upon  surfaces  exposed  normally 
to  its  direction  must  often  be  enormous.  In  the  example  of 
§  234,  although  the  gyratory  velocity  of  the  air  at  the  distance 
of  looo  meters  is  only  3  meters  per  second,  yet  by  theory  the 
velocity  at  the  distance  of  21.4  meters  is  140  meters  per  sec- 
ond, or  about  310  miles  an  hour.  This  by  the  preceding  for- 
mula and  the  table  would  give,  at  the  earth's  surface,  for  an 
average  temperature,  an  effective  force  in  moving  an  object  of 
about  300  pounds  for  each  square  foot  of  normal  surface  ex- 


3/8  TORNADOES. 

posed  to  the  wind.  But  if  the  body  were  a  sphere  it  would  be- 
only  half  as  much  for  each  square  foot  of  area  of  maximum 
section. 

In  the  case  of  the  velocity  of  the  ascending  current  of  176 
miles  per  hour  near  the  earth's  surface  obtained  upon  the  as- 
sumptions of  §  242,  Table  VII  gives  a  supporting  power  of 
more  than  90  pounds  to  the  square  foot. 

247.  Having  now  determined  the  force  of  an  ascending 
current  of  given  velocity  s  against  a  sphere  of  given  maximum 
sectional  area  A,  as  in  the  last  expression  of  p'  ,  this  becomes. 
the  supporting  power  of  an  ascending  current  in  keeping  such 
a  sphere  from  falling  to  the  earth.  The  mass  of  a  sphere  of 
pure  water  one  foot  in  diameter,  expressed  in  pounds  avoirdu- 
pois, is  62.43  X  0.5236  Da,  in  which  D  is  the  diameter  of  the 
sphere  in  feet,  62.43  being  the  mass  of  a  cubic  foot  of  water, 
and  0.5236  the  ratio  of  a  sphere  to  its  circumscribing  cube. 
Hence  the  mass  M  of  any  sphere  of  diameter  D  and  density  p, 
and  likewise  the  force  of  gravity  expressed  in  pounds,  taking 
no  account  of  the  slight  variations  of  gravity  at  different  lati- 
tudes and  altitudes,  is  M  —  32.69  D3  p. 

In  the  case  of  a  body  falling  through  the  atmosphere,  or 
any  other  resisting  medium,  the  velocity  of  the  body  is  acceler- 
ated until  the  resistance  becomes  equal  to  the  force  of  gravity, 
after  which  it  continues  uniform  unless  the  force  or  the  density 
of  the  medium  changes.  But  if  the  ascending  current  has  the 
same  velocity  as  that  with  which  the  body  would  fall  through 
it  after  the  velocity  becomes  uniform,  the  force/7  of  the  ascend- 
ing current  against  the  sphere,  which  is  the  resistance  in  the 
case  of  the  falling  body,-  is  equal  to  the  force  of  gravity,  and 
the  body  is  supported.  Hence,  putting  the  preceding  expres- 
sion of/'  equal  to  the  force  of  gravity,  M,  we  get 


as  the  condition  for  determining  the  diameter  of  a  sphere  of 
given  density  p  which  would  be  supported  by  an  ascending  cur- 


SUPPORTING  POWER   OF  ASCENDING   CURRENTS.      379* 

rent  of  velocity  s,  under  any  given  condition  of  pressure  P  and 
temperature  r. 

Since  A  is  the  maximum  section  of  the  sphere,  we  have 
A  =  O.7854/?2,  0.7854  being  the  ratio  of  the  circle  to  its  cir- 
cumscribing square.  With  this  value  of  A,  the  preceding  equa- 
tion gives 

_  0.0000396  P  s^ 
~  I +0.0042- P0p' 

Having  used  the  expression  of  p'  instead  of  /,  the  theoretical 
expression  of  the  force  of  the  wind,  this  expression  takes  into 
account  the  effect  of  friction  as  heretofore  determined. 

For  the  diameter  of  a  sphere  of  the  density  of  water,  which 
is  supported  by  an  ascending  current  of  100  miles  per  hour  near 
the  earth's  surface,  where  P  may  be  put  equal  to  P9,  assuming 
that  the  temperature  is  o°  C.,  we  get,  very  nearly,  D  =  0.4  of 
a  foot,  or  4.8  inches.  For  a  sphere  of  ice  of  density  0.92  at  the 
altitude  where  P  =  %P0,  it  gives  for  the  same  ascending  velocity 
D  =  0.215  of  a  foot,  or  2.58  inches. 

With  the  preceding  expression  the  values  of  D  in  Table  VII 
have  been  computed,  giving  the  diameters,  in  inches,  of  a  sphere 
of  the  density  of  water  which  would  be  supported  by  ascending 
currents  of  air  of  the  velocities  s  in  the  first  column,  at  the  alti- 
tudes where  the  barometric  pressures  are  as  given  at  the  heads 
of  the  columns,  the  temperatures  being  assumed  to  be  as  in  the 
table  of  §  13.  For  spheres  of  other  densities,  it  is  seen  from 
the  formula  the  tabular  numbers  must  be  divided  by  the  den- 
sity as  compared  with  water. 

248.  In  the  case  of  an  ascending  current  of  velocity  j,  a 
body  with  a  diameter  of  the  value  of  D  given  by  the  preceding 
formula,  or  by  Table  VII,  would  remain  suspended  in  the  air, 
but  if  the  ascending  velocity  were  increased,  the  body  would  be 
carried  up  at  such  a  rate  as  to  le«f  the  relative  ascending 
velocity  between  the  air  and  the  booy  equal  to  s.  According 
to  the  preceding  example  of  a  sphere  of  ice,  a  hailstone  of  the 
diameter  of  2.58  inches,  up  where  the  pressure  in  only  380  mm. 
would  be  sustained  in  the  air  at  the  same  level,  by  an  ascend- 


380  TORNADOES. 

ing  current  of  100  miles  per  hour,  but  if  this  current  were  in- 
creased to  no  miles,  then  the  hailstone  would  be  carried  up  at 
the  rate  of  10  miles  per  hour,  as  long  as  the  pressure  and 
density  were  not  sensibly  changed,  and  it  would  continue  to 
ascend  with  decreasing  velocity  until  the  value  of  P  in  the  pre- 
ceding expression  of  D  would  be  satisfied  for  D  =  0.215  and 
s  =  ioo. 

The  ascending  velocity  required  to  sustain  a  rain-drop  in 
the  air  is  given  by  the  preceding  formula  and  Table  VII.  If 
the  rain-drop  is  o.i  of  an  inch,  then  D  =  0.0083  °f  a  foot. 
With  this  value  of  D  the  preceding  formula  is  satisfied  up  at 
the  altitude  where  P  —  600  mm.  and  t  =  10°  C.,  with  the  value 
of  s  =  16.6,  which  is  a  very  gentle  ascending  current,  but  sufifi- 
•ciently  strong  to  prevent  the  falling  of  ordinary  rain-drops. 

Mr.  Dines  has  measured  rain-drops  as  small  as  0.0033  inch 
in  diameter.  Drops  of  this  size  satisfy  the  formula  up  where 
.P  •=.  600  mm.  with  a  value  of  s  =-3,  and  hence  an  ascending 
velocity  of  3  miles  per  hour  would  sustain  such  drops.  Mr. 
Dines97  has  also  measured  fog  particles  as  small  as  0.00062 
inch,  equal  0.0000517  of  a  foot.  With  this  value  of  D  the 
formula  at  an  altitude  where  P  =  600  mm.  gives  s  =  0.41. 
The  law  of  resistance  as  the  square  of  the  diameter  and 
velocity,  as  given  by  the  expression  of/7,  §  246  (for  A  is  as  D2) 
may  not  hold  very  accurately  for  so  small  particles,  but  the 
formula  applied  in  these  cases  at  least  shows  that  exceedingly 
small  ascending  velocities  are  sufficient  to  sustain  even  the 
larger  and  measurable  cloud  and  fog  particles  in  the  air,  and 
so  there  is  no  necessity  to  resort  to  the  old  and  improbable 
vesicular  theory  of  cloud  particles  in  order  to  account  for  the 
floating  of  clouds  in  the  air.  For  in  the  cyclone  and  cloud 
areas  we  know  there  are  always  ascending  currents,  and  in  the 
surrounding  parts  where  there  is  no  ascent  of  the  air,  or  gen- 
erally a  slight  descent,  there  is  a  clearing  off  from  the  descent 
'of  the  cloud  particles  innfthe  unsaturated  air  below,  where  they 
are  evaporated  and  converted  back  again  into  clear  and  trans- 
parent vapor.  Hence,  as  in  the  vertical  circulations  of  the 
•  atmosphere  the  slight  ascending  currents  in  some  places  give 


SUPPORTING  POWER   OF  ASCENDING  CURRENTS.      381 

rise,  first  to  haziness,  and  then  to  a  clouded  sky,  so  at  others, 
where  there  are  very  slowly  descending  currents,  the  sky  which 
previously  was  entirely  overcast  with  clouds  becomes,  somewhat 
all  at  once,  clear  from  the  vanishing,  and  not  from  the  passing 
over  of  the  clouds. 

The  size  of  rain-drops  in  all  cases  is  an  indication,  in  some 
measure,  of  the  velocity  of  the  ascending  currents.  Small  rain- 
drops indicate  that  the  ascending  current  is  so  feeble  that  they 
can  fall,  and  are  not  carried  up ;  but  where  only  very  large 
drops  fall,  the  indication  is  that  the  ascending  current  is  so 
strong  that  all  except  the  very  large  ones  are  either  carried 
upward,  and  in  the  case  of  a  tornado  outward  above  to  where 
the  ascending  currents  are  less,  or  else  are  sustained  in  the  at- 
mosphere until  by  the  contact  and  blending  with  them  of  other 
drops,  they  become  large  enough  to  fall. 

249.  Only  a  few  of  the  many  instances  of  observed  force  of 
the  wind  and  supporting  power  of  ascending  currents  in  tor- 
nadoes can  be  given  here,  for  the  literature  on  this  subject  has 
become  immense.  From  the  account  of  the  tornado  of  April 
1 6,  1875,  at  Walterborough,  S.  C.,69  the  following  facts  are 
taken  : 

The  Academy  and  seven  churches  were  totally  destroyed,, 
and  of  the  whole  number  of  ninety  dwellings  some  sixty  were 
torn  to  pieces  and  strewn  to  the  four  winds  of  heaven.  At 
least  5000  trees  in  the  village  were  scattered  in  every  direction. 
The  roar  of  the  wind  was  such  that  the  tremendous  crash  was 
heard  by  no  one.  One  gentleman  was  looking  from  his  piazza 
and  saw  large  trees  fall  in  his  yard,  but  heard  no  more  sound 
than  if  they  had  been  feathers. 

The  greatest  destruction  was  on  the  south  side  of  the  track. 
A  heavy  piece  of  timber  6  by  6  inches  and  40  feet  long,  weigh- 
ing 600  pounds,  was  carried  from  the  Episcopal  church  in  a 
direct  line  over  the  tops  of  houses  to  a  distance  of  440  yards  in 
a  direction  W.  10°  N.  The  wind  continued  in  its  first  direction 
for  a  few  seconds  only,  when  it  changed  to  the  north  with  in- 
creased fury.  A  large  4-horse  lumber  wagon,  weighing  3,500 


382  TORNADOES. 

dbs.,  was  lifted  over  a  6-foot  fence  and  carried  60  feet  from  its 
-original  position. 

A  chicken  coop,  box  4  by  4  feet,  weight  75  Ibs.,  was 
•carried  4  miles.  Hickory  trees,  54  inches  in  circumference  at 
butt,  weight  3000  pounds,  were  lifted  out  of  the  ground  and 
•carried  up  a  bank  10  feet  high.  A  cart  weighing  600  pounds 
was  carried  up  in  the  whirl,  torn  to  pieces,  and  the  tire  of  one 
wheel  found  1320  yards  distant.  Dead  sheep  were  found  with 
wool  off  the  hide.  Geese  plucked  of  feathers,  as  if  picked  by 
hand. 

From  the  account  of  the  tornado  of  Aug.  9,  1878,  at  Wal- 
lingford,  Conn.,70  the  following  statements  are  gleaned :  The 
:great  power  of  the  wind  at  one  place  was  illustrated  by  the 
carrying  of  a  large  oak  tree  so  far  that  its  place  of  growth 
could  not  be  found.  Persons  witnessing  it  said  that  two  cur- 
rents of  air  seemed  to  unite  at  this  point,  where  the  valley 
grew  narrower. 

The  indraught  reaching  down  Old  Colony  street  was  severe 
enough  to  take  large  elm  trees  and  wrench  them  off  at  some 
distance  from  the  ground.  Along  this  street  where  the  roots 
of  trees  were  strong  and  well  planted,  the  limbs  only  were 
affected,  the  appearance  being  that  the  force  was  exerted  some 
feet  above  the  surface.  A  barn  was  carried  bodily  away  and 
no  parts  of  it  afterward  recognized.  Mr.  Vasseur's  house  was 
lifted  up  and  the  parlor  floor  arched  upward.  An  elm  tree, 
measuring  9  feet  in  circumference,  was  broken  off  9  or  10  feet 
from  the  ground. 

Pieces  of  timber  and  scantling  were  imbedded  in  apple  trees 
so  far  (fully  6  or  7  inches  deep),  that  in  efforts  to  pull  them  out 
they  were  broken  off.  An  iron  rowboat,  said  to  weigh  about 
•80  or  85  pounds,  was  lifted  from  the  water  of  the  pond  and  car- 
ried by  the  force  of  the  wind  225  feet.  A  large  apple  tree, 
weighing  nearly  1500  pounds,  was  carried  20  feet  due  north. 

The  arching  up  of  Mr.  Vasseur's  parlor  floor  was,  no  doubt, 
•caused  by  the  expansion  of  the  air  beneath,  from  the  sudden 
removal  of  the  surrounding  pressure  (§  236). 

250.  The  following  facts  are  taken  from  the  account  of  the 


SUPPORTING   POWER   OF  ASCENDING   CURRENTS.      383 

tornado  at  Mount  Carmel,  Illinois,  June  4,  1877:"  The  houses 
on  the  south  side  of  the  street  were  totally  destroyed,  and 
bricks  and  other  objects  hurled  with  great  force  northward 
against  the  buildings,  somewhat  damaged  but  left  standing,  on 
the  opposite  side  of  the  street.  A  brick  moving  at  an  angle  of 
15°  or  20°  with  the  horizon,  entered  the  Harris  house  through 
the  weather-boarding,  lath  and  plastering,  crossed  two  rooms, 
a  distance  of  27  feet,  and  lodged  in  a  rear  wall  without  break- 
ing even  the  corners  from  the  brick.  From  the  large  and  cir- 
cular aperture  through  which  the  brick  entered  it  was  thought 
that  it  must  have  whirled  rapidly  in  its  transit.  So  great  was 
its  velocity,  that  the  laths  were  cut  quite  smoothly  without 
cracking  the  adjoining  plastering. 

Lewis  Gott  saw  the  tornado  strike  his  house,  his  point  of 
observation  being  one  square  north.  As  he  described  it,  the 
house  appeared  to  go  up  bodily  and  plunge  into  the  cloud. 
Only  a  very  small  portion  of  it  was  ever  seen  afterward  to  be 
recognized. 

Although  many  small  objects  were  thrown  outward  by  the 
whirl  of  the  tornado,  yet  the  general  tendency  of  trees  and 
prostrate  buildings  was  inward  toward  the  centre  of  the  track, 
this  effect  being  more  noticeable,  however,  on  its  southern  than 
on  its  northern  side. 

Objects  were  carried  to  great  distances.  A  piece  of  tin  roof 
was  carried  17  miles  N.E.  The  spire,  vane,  and  gilded  ball  of 
the  Methodist  Church  were  found  at  the  distance  of  15  miles 
N.E.  A  letter  was  carried  by  the  wind  45  miles  in  the  direc- 
tion of  N.N.E.  A  paper  sack  of  flour  was  found  nearly  5  miles 
distant  in  Indiana. 

The  accompanying  plate,  copied  from  the  Report  of  the 
Chief  Signal  Officer  for  1877,  shows  the  destructive  violence  of 
this  tornado  in  a  narrow  path  where  it  passed  through  Mount 
Carmel. 

251.  The  following  extracts  are  taken  from  an  account  by 
H.  C.  Hovey  of  the  tornado  at  St.  Cloud  and  Sauk  Rapids, 
Minn.,  which  took  place  on  April  14,  i886.76 

"  During  the  day  a  remarkably  high  temperature,  for  the  season,  had 


384 


TORNADOES. 


SUPPORTING  POWER   OF  ASCENDING   CURRENTS.      385 

prevailed,  the  mercury  rising  as  high  as  80°,  and  the  air  was  sultry  and 
oppressive.  At  3  P.M.  observers  saw  dark  banks  of  struggling  clouds 
overhanging  the  ridge  that  in  ancient  times  used  to  be  the  river  limit, 
and  there  were  apprehensions  of  impending  danger.  Suddenly  the  clouds 
began  to  revolve,  while  sharp  points  shot  downward,  until  a  whirling  fun- 
nel-shaped mass  was  formed  above  a  basin  amid  the  hills,  that  seems  to 
have  furnished  the  cradle  for  the  ensuing  tornado.  Its  first  condition 
was  undoubtedly  that  of  a  simple  whirlwind,  having  a  diameter  of  about 
looo  feet,  which  uprooted  or  twisted  off  nearly  every  tree  in  its  circle, 
overturned  the  monuments  in  the  adjoining  Masonic  cemetery,  and  tore 
up  the  boulders  from  the  ground.  Thence  it  moved  slowly  and  majesti- 
cally along  at  the  rate  of  about  12  or  15  miles  per  hour,  but  with  an  in- 
conceivably rapid  rotary  motion  upon  its  vertical  axis,  confining  itself 
for  some  distance  to  a  path  hardly  more  than  150  feet  wide.  Hundreds 
of  people  took  timely  warning  and  got  out  of  the  road  of  the  moving 
column  of  cloud,  whose  general  trend  was  toward  the  northeast.  Hav- 
ing wrecked  the  Catholic  Church  on  Calvary  Hill,  and  also  several  farm- 
houses, it  entered  a  portion  of  the  city  of  St.  Cloud  mainly  occupied  by 
foreigners,  whose  frame  cottages  were  strewn  over  the  plain  indiscrimi- 
nately, leaving  nothing  but  the  cellars  to  mark  the  sites  of  the  houses. 

"  I  noticed  but  one  exception  to  this  general  work  of  complete  demo>- 
lition,  and  that  was  a  house  that  had  been  whirled  about  end  for  end  and 
left  on  its  foundation  as  a  wreck.  Reaching  the  freight  depot  of  the 
Manitoba  R.  R.  the  wind  tore  to  pieces,  and  overturned  the  long  line  of 
freight  cars,  carried  the  trucks  away,  and  even  in  places  wrenched  the 
iron  rails  from  the  ties. 

"  The  tornado  struck  the  Mississippi  River  at  a  point  opposite  the 
village  of  Sauk  Rapids,  and  fishermen  who  were  in  full  view  of  the  cross- 
ing aver  that  for  a  few  moments  the  bed  of  the  river  was  swept  dry ;  and 
in  corroboration  of  this  remarkable  statement  they  showed  me  a  marshy 
spot  where  no  water  had  been  before  this  event  took  place.  Two  spans 
were  torn  away  from  the  substantial  wagon  bridge  below  the  rapids,  one 
span  being  hurled  up  stream  and  the  other  down  it  by  the  rotary  motion 
of  the  blast;  and  great  blocks  of  granite  being  also  torn  bodily  out  from 
the  piers.  The  large  flour  mill  near  the  bridge  was  levelled.  The  depot 
of  the  Northern  Pacific  R.  R.  was  demolished,  and  the  central  portion 
of  the  village  itself  was  attacked  with  the  greatest  violence.  Being  the 
county  seat,  the  court-house  was  located  here,  a  substantial  structure,  of 
which  only  the  vault,  six  iron  safes,  and  the  calaboose  were  left — the 
latter  turned  upside  down.  A  fine  new  school-house,  costing  $15,000, 
was  completely  swept  away.  The  Episcopal  Church  was  so  utterly  re- 
moved that  the  sole  relic  thus  far  found  is  a  battered  communion  plate. 
The  floor  of  the  skating-rink  is  all  that  is  left  of  that  structure.  Stores,. 


386  TORNADOES. 

hotels,  a  brewery,  and  four-fifths  of  the  residences  in  the  village  were 
scattered  as  rubbish  along  the  hillsides,  or  borne  away  for  miles  through 
the  air. 

"One  of  the  saddest  of  the  tragedies  marking  this  wide  disaster  took 
place  at  a  farm-house  in  the  country,  about  16  miles  north  of  Sauk  Rapids, 
where  a  wedding  party  of  30  persons  were  assembled.  The  ceremony 
was  just  concluded,  and  the  officiating  clergyman  was  offering  prayer 
when  the  building  was  struck  by  the  tornado.  The  bridegroom  was  killed 
ouiright,  as  were  also  15  others ;  7  more  victims  have  since  died,  and  only 
one  of  the  company  escaped  severe  injury  of  some  kind." 

The  number  of  killed  at  Sauk  Rapids  was  39,  and  about  100 
injured  more  or  less. 

252.  On  the  2Qth  and  3Oth  of  May,  1879,  there  were  many 
very  destructive  tornadoes  in  the  States  of  Kansas,  Nebraska, 
Iowa,  and  Missouri,  which  were  thoroughly  investigated  by 
Sergeant  (now  Lieutenant)  F.  P.  Finley  of  the  Signal  Service, 
and  the  results  given  in  a  published  report.72  From  this  lengthy 
report  of  116  quarto  pages,  containing  a  great  number  and  va- 
riety of  very  important  and  astonishing  facts  in  relation  to  tor- 
nadoes, the  following  few  are  selected  as  examples  of  the  great 
force  of  the  wind  and  its  raising  and  supporting  power  in  a 
tornado,  and  in  corroboration  of  the  theoretical  deductions  in 
preceding  pages : 

From  the  account  of  the  Lee  Summit  tornado  on  the 
western  border  of  Missouri  the  following  extracts  are  taken : 

"  Among  several  of  the  peculiar  manifestations  of  the  wind's  force  at 
this  place,  I  relate  the  following:  150  feet  N.E.  of  the  house  and  10  feet 
W.  from  the  stable,  a  large  gate  was  carried  200  feet  to  the  S.E.  and  torn 
to  pieces  without  injuring  the  stable.  A  heavy  lumber  wagon,  standing 
behind  the  corn-crib  and  at  a  distance  of  155  feet  east  of  the  house,  was 
lifted  up  bodily  and  carried  to  the  S.E.  over  a  corn-field  a  distance  of  100 
feet,  without  injury.  Two  window-panes  were  blown  from  a  sash  on  the 
W.  side  of  the  house  and  carried  inside  without  breaking  them,  while  two 
out  of  the  N.  window  were  found  broken.  A  large  well-curb  lying  E.  of 
the  house  15  feet  was  carried  one-fourth  mile  to  the  S.E.  and  lodged  in  a 
wheat-field.  A  heavy  sulky  cultivator,  weighing  about  600  pounds,  was 
carried  free  from  the  ground  a  distance  of  86  yards  to  the  S.S.E.  and 
broken  by  the  fall.  Another  one  standing  near  the  corn-crib  was  partly 
carried  and  partly  rolled  along  a  distance  of  about  60  rods  to  the  S.E.,  and 


-SUPPORTING  POWER   OF  ASCENDING   CURRENTS.      387 

then  literally  twisted  to  pieces  and  the  debris  scattered  about  over  a  field 
of  12  acres,  apparently  in  circles." 

"  The  following  will  indicate  some  of  the  peculiar  freaks  of  the  storm  : 
A  carpet  upon  the  floor  of  the  Jog  part  of  the  house,  and  securely  tacked 
about  the  edges,  was  taken  up  and  carried  out  of  the  house  without 
being  torn.  A  new  sewing-machine  was  broken  into  forty  or  fifty  pieces. 
Five  feather  beds  were  torn  into  strips  and  the  feathers  scattered  broad- 
cast over  the  country.  Several  garments  were  carried  four  or  five  miles 
to  the  N.E.  An  iron  kettle,  holding  15  gallons,  was  found  broken  into 
six  pieces*  and  scattered  about  in  several  directions.  A  lo-gallon  keg 
filled  with  vinegar  was  carried  to  the  N.E.  40  rods.  A  large  iron-bound 
trunk,  fitted  with  an  extra  heavy  lock,  was  torn  to  pieces,  and  the  lock 
found  a  half  mile  to  the  N.E.  sticking  into  a  rail.  Several  photographs 
^which  were  known  to  have  been  securely  placed  in  an  album  in  the 
trunk,  were  found  over  four  miles  to  the  N.E.  A  watch  in  the  vest  of 
Mr.  J.  H.  Warden,  was  blown  50  yards  to  the  N.E.  and  found  covered 
ivith  mud,  but  the  vest  was  carried  to  the  E.  20  yards.  Several  chickens 
were  carried  to  the  N.E.,  from  one-fourth  to  one-half  mile  and  entirely 
stripped  of  feathers.  Two  stoves  were  broken  into  small  pieces,  and  one 
standing  near  the  middle  of  the  house  was  uninjured.  Heavy  bed-quilts 
were  so  filled  with  mud  that  when  dry  they  were  as  stiff  and  hard  as 
boards.  A  lumber  wagon  was  carried  to  the  N.W.  10  rods,  the  box  torn 
to  pieces,  and  nearly  all  the  spokes  taken  out  of  the  wheels.  An  iron- 
beam  plow,  25  feet  W.  of  the  house,  was  not  moved  or  injured,  and  aseed- 
•drill  and  harrow  near  the  barn  were  also  untouched." 

According  tot  Mr.  Richardson's  account,  at  Mr.  Hutchins's, 

"trees  and  broken  timber  could   be  seen  jerked   up  into  the  vortex, 
whirled  around  with  terrible  fury,  and  then  thrown  outward  at  the  top." 

253.  The  following  instances  of  the  great  power  and  fury 
of  a  tornado  are  taken  from  the  account  of  the  Irving  tor- 
nado : 72 

"  The  houses  of  Edward  Wentworth,  Gavin  Reed,  Robert  Reed,  and 
Wesley  Cooper,  situated  in  the  bottom  of  a  'draw  '  leading  into  Game 
Fork  Creek  from  Timber  Creek,  in  an  E.N.E.  direction,  were  next 
reached  and  fairly  ground  to  pieces.  Hardly  a  board  6  feet  long  was  left 
near  the  foundation  of  any  of  the  buildings.  The  funnel  as  it  passed  the 
high  '  divide  '  to  the  '  draw '  perceptibly  widened  at  the  bottom ;  but 
without  bodily  swooping  downward  at  once,  it  drew  the  buildings  up 
into  its  vortex  and  then  twisted  them  to  pieces.  The  house  of  Robert 
Reed,  16  by  24  feet,  and  one  and  a  half  stories  high,  was  lifted  up  as 
easily  as  a  feather,  and  without  at  first  cracking  the  timber.  So  quickly 


388  TORNADOES. 

was  it  done,  that  before  Mr.  Reed,  who  was  within,  knew  his  danger,  the 
building  had  risen  a  height  of  25  feet  or  more.  The  house  being  then 
enveloped  in  darkness,  and  not  knowing  what  had  happened,  he  started 
for  the  door,  thinking  it  time  to  make  good  his  escape,  when,  instead  of 
stepping  out  upon  the  ground,  as  he  expected,  he  fell  the  above  distance, 
injuring  himself  severely." 

After  giving  various  other  details  with  regard  to  this  tor- 
nado, it  is  further  stated  : 

"Going  back  to  the  funnel  cloud  where  we  left  it  at  its  entrance 
upon  Game  Fork  Creek,  we  find  that  it  followed  the  bed  of  the  stream 
very  closely,  hugging  the  eastern  bluffs  with  such  tenacity  that  it  ripped 
up  nearly  every  tree  along  their  sides  and  withered  the  tough  prairie 
grass.  Persons  who  watched  its  progress  along  this  portion  of  its  track 
stated  that  the  demoniac  fury  of  the  cloud  was  appalling ;  whirling  with 
most  frightful  rapidity,  the  intense  black  column  would  at  times  seem  to 
level  the  whole  bluff  as  it  disappeared  from  view  within  the  huge  rolling 
mass  of  darkness.  The  eastern  bank,  covered  with  a  luxuriant  growth  of 
timber,  would,  as  the  cloud  moved  along,  successively  emerge  from  its 
awful  baptism  swept  clean  to  the  soil.  While  this  terrific  manifestation 
of  force  was  going  on  along  the  stream,  westward  over  the  valley,  a  dis- 
tance of  60  rods,  only  a  gentle  wind  was  experienced." 

254.  Of  the  Stockdale  tornado,  when  it  struck  Mr.  Con- 
dray's  house,  it  was  said 

"that  the  roof  was  carried  to  a  perpendicular  height  of  nearly  200  feet. 
....  The  roof  was  lifted  as  easily  as  if  it  had  been  a  feather,  shot  up- 
ward in  the  very  centre  of  the  cloud,  and  fairly  ground  to  pieces,  the 
debris  whirling  in  circles  about  the  upper  portion  of  the  cloud,  and  finally 
dropping  to  the  ground  one-fourth  of  a  mile  from  the  centre  of  the. 
storm's  path." 

In  the  Delphos  tornado,72 

"two  new  lumber  wagons  were  carried,  one  35  and  the  other  40  rods  to 
the  N.W.,  and  broken  into  pieces  ;  one  of  the  wheels,  nearly  whole,  was 
found  a  distance  of  one  mile  N.W.  of  the  barn  ;  the  other  wheels  were 
broken  from  the  axles,  divested  of  their  spokes,  and  the  large  heavy  iron 
tires  were  bent  into  every  shape.  A  log  from  the  barn,  12  feet  long  and 
10  inches  in  diameter,  was  carried  320  yards  to  the  N.N.W.  The  front 
iron  axle  of  a  top  buggy  (i£  inches  in  diameter)  was  found  bent  double, 
the  two  ends  crossing  each  other,  and  both  wheels  were  torn  off  even  to 
the  hubs." 

It  is  also  stated  of  the  same  tornado  that  heavy  cast-iron 


SUPPORTING  POWER  OF  ASCENDING  CURRENTS.       389 

wheels  broken  from  a  large  harvester,  and  weighing  200  pounds 
each,  were  carried  half  a  mile. 

In  the  Barnard  tornado 

•"a  large  government  wagon-box,  covered  with  about  200  pounds  of  iron 
in  the  way  of  fasten  ings,  .was  carried  away  from  near  the  corn-house,  and 
no  portion  of  it  afterward  discovered.  Two  sulky  cultivators,  weighing 
between  400  and  500  pounds  each,  were  broken  into  pieces  and  portions 
carried  to  the  E.  for  a  distance  of -one-fourth  of  a  mile." 

The  Gentry  County  tornado,  in  crossing  the  river  at  Green- 
well  ford,  4  miles  S.  of  Albany, 

•"lifted  the  new  iron  bridge  of  160  feet  span  and  weighing  120  tons,  from 
the  stone  pier  upon  which  it  rested,  carrying  it  into  the  bed  of  the  river 
without  overturning  it.  The  structure  was  strongly  bolted  to  the  abut- 
ment at  one  end,  while  the  other  end  rested  on  rollers  at  the  opposite 
abutment  to  allow  for  the  expansion  and  contraction  of  the  iron  string- 
gers." 

255.  The  prostrating  force  of  horizontal,  and  the  raising  and 
supporting  power  of  ascending,  currents,  as  manifested  in  the 
preceding  extracts  from  the  accounts  of  the  observed  phenom- 
ena of  tornadoes,  are  mostly  explicable  from  the  theoretical 
deductions  of  the  preceding  pages.  By  the  law  of  rv  =  c,  §  232, 
we  have  seen  that  where  there  is  a  centripetal  force  and  an 
initial  gyratory  motion,  even  very  small  at  a  considerable  dis- 
tance from  the  centre,  the  velocity  becomes  enormously  great 
near  the  centre,  and  there  is  a  great  concentration  of  the 
energy  there.  The  assumed  example  of  §  234,  in  which  we  get 
a  theoretical  velocity  of  140  meters  per  second  at  the  distance 
of  21  meters  from  the  centre,  is  not  an  improbable  one,  which 
can  rarely  occur  in  nature,  but  there  are  probably  cases  which, 
after  making  all  due  allowance  for  friction,  may  give  much 
greater  velocities  at  that  distance,  and  these  are  enormously 
increased  still  nearer  the  centre.  But  with  this  velocity  we 
have  seen,  §  246,  the  force  exerted  upon  each  square  foot  of 
normal  surface  is  about  300  pounds.  The  force  of  such  a  veloci- 
ty, therefore,  on  the  side  of  a  large  building,  although  it  were 
of  great  weight,  is  amply  sufficient  to  overthrow  it  and  carry  it 
along  until  it  is  broken  to  pieces  and  the  parts  scattered  in 
many  directions. 


390  TORNADOES. 

Such  a  force  also  is  sufficient  to  move  cars  from  the  track 
of  a  railroad,  of  which  we  have  several  instances  in  the  preced- 
ing extracts,  and  carry  them  to  a  considerable  distance. 

According  to  the  preceding  law,  it  is  seen  how  the  kinetic 
energy  of  a  tornado  may  be  enormously  great  in  the  vortex  of 
a  tornado,  while  at  a  very  short  distance  there  is  scarcely  any- 
perceptible  wind.  Thus  in  the  case  of  the  Irving  tornado* 
(§  253)»  at  a  distance  of  only  60  rods  from  the  vortex  and  place 
of  greatest  devastation,  only  a  gentle  wind  was  experienced. 
Hence  the  track  of  destructive  violence  of  a  tornado  is  always 
narrow.  According  to  Finley,73 

"  The  width  of  the  path  of  destruction,  supposed  to  measure  the  dis- 
tance between  the  areas  of  sensible  winds  on  the  sides  of  the  storm's. 
centre,  varied  from  40  to  10,000  feet,  the  average  being  1085  feet." 

A  wind  with  a  velocity  of  140  meters  per  second  would  of 
course  have  much  less  force  against  a  tree,  even  with  foliage, 
than  against  a  solid  barrier,  since  much  of  the  air  would  pass 
through  the  tree,  and  so  would  exert  no  force  against  it  except 
by  friction  upon  the  air  which  is  obstructed  and  does  not  pass. 
But  making  an  allowance  of  one-half,  we  yet  have  an  enormous 
force  against  the  top  part  of  the  tree,  which  acts  with  a  lever- 
age upon  the  stem  in  breaking  it,  and  upon  the  roots  of  the 
tree  in  overturning  it. 

But  we  have  reason  to  think  that  the  velocity  of  the  air  in 
a  tornado,  especially  very  near  its  centre,  is  often  much  more 
than  140  meters  per  second,  and  so  by  Table  VII,  the  forces, 
exerted  against  the  obstructions  are  still  much  greater. 

256.  From  the  theoretical  result  of  the  example  in  §  242  of 
an  ascending  velocity  of  176  miles  per  hour,  which  is  based, 
upon  no  unreasonable  assumptions,  but  upon  such  as  can  by 
no  means  be  regarded  as  extreme  ones,  we  have  reason  to 
think  that  the  velocity  of  the  ascending  current  in  the  central 
part  of  a  tornado  is  often  enormously  great.  Even  the  veloci- 
ty of  176  miles  per  hour,  gives  a  lifting  and  supporting  force 
near  the  earth's  surface  of  more  than  90  pounds  to  a  square 
foot  (§  246).  ^Extreme  cases  may  even  give  forces  several 
times  greater  than  this. 


SUPPORTING  POWER   OF  ASCENDING  CURRENTS.      39 1 

The  nearly  horizontal  and  gyratory  currents  at  a  little  dis- 
tance from  the  centre  near  the  earth's  surface,  where  they  are 
more  radial  than  at  a  small  altitude  above  the  earth's  surface, 
necessarily  become  largely  ascending  currents  also  as  they  ap- 
proach the  vortex  of  the  tornado,  and  so,  with  the  enormous 
forces  of  so  great  velocities,  readily  carry  large  and  heavy 
bodies  into  the  vortex  and  up  in  the  interior  of  the  tornado, 
and  support  them  at  a  considerable  altitude  above  the  earth's 
surface,  until,  in  the  progressive  motion  of  the  tornado,  they 
have  been  carried  to  a  great  distance.  As  the  altitude  is  in- 
creased and  the  density  of  the  air  diminished,  the  formula  and 
Table  VII  show  that  the  supporting  power  of  the  same  veloc- 
ity is  diminished,  and  in  proportion  to  the  density.  It  may 
happen,  therefore,  that  the  raising  and  supporting  force  of  the 
tornado  may  be  such  as  to  raise  a  body  and  support  it  at  a 
considerable  altitude,  but  not  be  able  to  raise  it  up  to  where 
the  currents  above  are  outward  from  the  centre,  and  so  it  has 
to  remain  at  some  distance  above  the  earth's  surface,  within 
the  vortex  of  the  tornado,  where  it  is  at  the  same  time  whirled 
rapidly  round  and  round  the  centre,  until,  from  some  increase 
of  the  energy  of  the  tornado,  it  is  carried  up  and  out  above, 
where  the  ascending  current  is  not  strong  enough  to  prevent 
its  falling,  or  until  for  some  reason  the  energy  of  the  tornado 
is  so  exhausted,  and  the  velocity  of  the  ascending  current  so 
diminished,  that  it  falls  directly  back  in  the  interior  and  central 
part.  In  either  case  the  tornado  may  have  progressed  mean- 
while to  a  long  distance.  Smaller  and  lighter  bodies  are  of 
course  carried  up  at  once  to  great  altitudes,  if  the  ascending 
currents  extend  up  so  high,  but  these  may  be  retained  for  a 
considerable  time  in  the  central  region  of  the  tornado  above, 
where  the  motion  is  much  more  gyratory  than  radial,  before 
they  get  so  far  from  the  centre  that  the  ascending  currents  do 
not  keep  them  from  dropping  down  ;  for  the  lighter  bodies 
have  to  be  carried  out  to  a  much  greater  distance  from  the  cen- 
tre before  they  can  fall. 

257.  There  is  not  much  difficulty,  therefore,  in  accounting 
for  the  sustaining  in  the  air  and  the  transportation  of  light,* 


392  TORNADOES. 

and  even  heavy,  bodies  to  a  great  distance.  Take,  for  instance, 
the  heavy  piece  of  timber  6  by  6  inches  and  40  feet  long, 
weighing  600  pounds,  which  was  carried  from  the  Episcopal 
Church  over  the  tops  of  houses,  §  249.  While  it  was  horizontal 
it  offered  a  surface  of  20  square  feet  to  the  wind.  By  Table 
VII  an  ascending  velocity  of  100  miles  per  hour  would  raise 
and  support  a  weight  of  600  pounds  with  a  normal  surface  of 
20  square  feet  exposed  to  the  current,  and  this  may  be  con- 
sidered as  no  unusual  velocity  of  the  ascending  air  in  a  tor- 
nado. The  same  velocity  perhaps  was  sufficient  to  carry  up 
the  cart  weighing  600  pounds,  as  the  amount  of  surface  ex- 
posed to  the  current  was  probably  at  least  20  square  feet. 
Also  a  much  smaller  velocity  would  raise  and  sustain  the 
chicken  coop  4  by  4  feet,  weight  75  pounds,  while  being  car- 
ried 4  miles. 

No  unusual  velocity,  likewise,  was  necessary  to  raise  and 
keep  up  in  the  air  the  tin  roof  at  Mt.  Carmel,  §  250,  while  it 
was  carried  17  miles  N.E.,  or  the  spire,  vane  and  gilded  ball  of 
the  Methodist  Church  while  being  carried  15  miles  N.E.,  or  a 
paper  sack  of  flour  while  being  transported  5  miles. 

In  the  same  manner  the  lifting  and  carrying  away  of  the 
heavy  lumber  wagon  at  Lee's  Summit,  §  252,  or  the  well-curb, 
or  the  cultivator  weighing  600  Ibs.,  may  be  accounted  for,  for 
we  can  assume  as  probable  an  ascending  velocity  of  much  more 
than  100  miles  per  hour,  if  necessary. 

The  iron  bridge  weighing  1 20  tons,  which  was  lifted  by  the 
Gentry  County  tornado,  §  254,  although  of  great  weight,  had 
also  a  great  amount  of  surface  exposed  to  the  ascending  cur- 
rent. If  we  suppose  that  there  was  a  weight  on  the  average 
of  300  pounds  to  the  square  foot,  then  according  to  computa- 
tions §  247,  and  to  Table  VII,  an  ascending  velocity  of  about  320 
miles  per  hour  would  be  necessary  to  lift  it.  This  is  perhaps 
an  extremely  great  velocity,  but  the  weight  of  the  bridge  may 
have  been  much  less  than  that  assumed  above,  and  so  the 
ascending  velocity  required  much  less. 

258.  We  now  see  how  a  body  may  be  raised  up  and  sus- 
tained in  the  atmosphere  when  once  up  where  there  are  rap- 


SUPPORTING  POWER   OF  ASCENDING   CURRENTS.      393 

idly  ascending  currents,  as  in  the  case  of  the  iron  bridge  above, 
but  it  remains  to  explain  how  bodies  close  on  the  earth's 
surface,  where  there  cannot  be  such  currents,  are  raised  bodily 
and  vertically  up  into  the  air.  Several  examples  of  this  sort 
are  given  in  the  preceding  extracts.  The  house  of  Lewis  Gott 
appeared  to  go  up  bodily  and  plunge  into  the  cloud  (§  250),  and 
in  the  Lincoln  County  tornado,  Mr.  Moore's  house,  200  yards 
west  of  the  storm's  centre,  12  by  30  feet  and  one  and  a  half 
stories  high,  "  was  lifted  bodily  and  carried,  with  the  entire  fam- 
ily in  it,  to  the  centre  of  the  track,  in  a  direction  a  little  S.  of 
E.,  where  it  went  to  pieces."72  The  house  also  of  Robert  Reed 
and  of  others  was  lifted  up  as  easily  as  a  feather  (§  253),  and 
likewise  the  roof  of  Mr.  Condray's  house  (§  254),  in  the  Stock- 
dale  tornado.  In  the  account  of  the  Irving  tornado  it  is  also 
stated,"  that 

"  the  house  of  Mr.  Morgan  stood  nearly  in  the  storm's  centre.  The  wind 
first  struck  it  on  the  E.  side,  lifting  it  bodily  up  to  the  W.,  off  the  foun- 
dation, when  it  disappeared  out  of  sight  in  the  dark  boiling  mass  of 
whirling  clouds.  Mr.  Morgan  and  family  were  in  the  cellar  and  saw  the 
house  pass  from  over  their  heads  in  the  manner  above  described." 

In  the  rapid  gyrations  of  the  vortex  of  a  tornado,  where 
there  are  numerous  inequalities  of  the  surface  and  substantial 
building  obstructions,  the  horizontal  currents  may  be  abruptly 
deflected  upward  so  as  to  give  a  strong  vertical  current  very 
near  the  earth's  surface,  by  which  objects  may  receive  an  up- 
ward start,  but  there  are  cases  in  which  buildings  seem  to  be 
drawn  vertically  upward  into  the  vortex  of  the  tornado  from  a 
level  surface  where  there  are  no  inequalities  and  obstructions 
of  this  sort. 

Let  us  suppose  that  a  tornado,  by  its  rapid  gyratory  motion 
in  the  open  air  above  the  earth's  surface  and  down  to  very 
near  the  surface,  brings  down  the  horizontal  and  disturbed  iso- 
baric  surface  AB  in  the  figure  following  to  the  earth's  surface, 
DE,  or  nearly,  in  the  form  of  the  curved  lines  ae  and  bf,  as  ex- 
plained in  §  233,  but  that  near  the  earth's  surface  in  the  stra- 
tum of  air  between  the  points  e  and  /and  the  surface  DE  there 
is  little  or  no  gyratory  motion.  This  would  be  very  much  less 


394 


TORNADOES. 


here  than  above,  on  account  of  the  friction  of  the  earth's  sur- 
face, if  even  the  tornado  were  stationary,  but  in  its  progressive 
motion,  carried  along  by  the  general  progressive  currents 
above,  the  rapid  whirl  of  the  air  above  does  not  have  time  to 
communicate  such  gyratory  motion  to  the  lower  stratum  of  air, 
which  has  less  progressive  motion,  for  the  vortex  above  is  being 
continually  brought  over  new  portions  of  the  stratum  below. 


Fig.  2. 

Between  the  points  e  and/,  say  at  the  height  of  1 50  feet  above  the 
earth's  surface,  there  may  be  nearly  a  vacuum,  while  at  the  earth's 
surface,  at  c,  the  pressure  and  density  are  very  nearly  the  same  as 
at  D  and  E,  since  there  is,  at  least  at  first,  scarcely  any  gyratory 
motion  to  counteract  the  horizontal  communication  of  the  press- 
ure from  D  and  E  to  c.  Let  us  suppose  that  instead  of  a  vacu- 
um the  barometric  pressure  between  e,  and/is  1 5  inches,  while  at 
c  it  is  30  inches.  There  is  then  a  decrease  of  barometric  press- 
ure between  c  and  the  central  part  of  the  vortex  at  the  level 
of  e  and  /of  15  inches,  in  150  feet,  or  one  inch  for  each  ten 
feet,  supposing  the  rate  of  decrease  to  be  the  same  through  the 
whole  vertical  space  of  150  feet.  If  now  there  is  a  cubical 
body,  of  no  very  great  weight  or  solidity,  as  a  wooden  house, 
with  a  linear  dimension  of  20  feet,  at  the  point  c  under  the  vor- 
tex, and  resting  on  or  being  very  near  the  earth's  surface,  then 
the  height  of  this  body  being  20  feet,  the  upward  pressure  at 
the  bottom  is  nearly  15  pounds  to  the  square  inch,  being  the 
ordinary  air  pressure  at  the  earth's  surface,  while  at  the  top, 
since  the  barometric  pressure  is  decreased  two  inches,  or  one 


GYRATORY  AND  PROGRESSIVE  MOTIONS.  395 

fifteenth  of  the  whole  at  the  earth's  surface,  the  pressure  to  the 
square  inch  is  only  14  pounds.  Hence  the  upward  pressure  on 
the  lower  surface  is  one  pound  to  the  square  inch  greater  than 
the  downward  pressure  on  the  upper  surface,  and  the  force 
which  tends  to  raise  the  whole  body  vertically  upward  into  the 
vortex  at  the  level  of  e  and/,  is  one  pound  to  the  square  inch,, 
or  nearly  30  tons  for  the  whole  body  with  a  superficial  area  at 
the  bottom  and  top  of  403  square  feet.  This  would  be  much 
more  than  sufficient  to  raise  vertically  upward  from  the  earth's 
surface  any  wooden  structure  of  those  dimensions,  and  hence, 
from  this  assumed  example  and  estimated  force,  it  is  seen  how 
bodies  upon  and  close  to  the  earth's  surface,  where  there  can  be 
little,  if  any,  ascending  velocity  of  the  air,  get  a  start  upward. 
When  once  a  little  distance  up,  where  the  velocity  of  the  as- 
cending current  in  consequence  of  this  rapid  decrease  of  press- 
ure is  very  great,  bodies  are  raised  and  sustained  by  the  force 
of  the  current,  as  already  explained. 

RESULTANTS   OF  GYRATORY  AND   PROGRESSIVE   MOTIONS. 

259.  According  to  Finley,"  of  the  600  tornadoes  upon  which 
he  reported,  "  the  rotary  movement  of  the  whirling  cloud  was 
invariably  from  right  to  left,  or  the  opposite  movement  of  the 
hands  of  a  watch."  This  indicates  either  that  the  earth's  rota- 
tion on  its  axis,  as  in  cyclones,  must  determine  the  direction, 
or  that  the  atmosphere  has  numerous  whirls  in  this  direction, 
the  results  of  previous  cyclonic  gyrations  which  have  not  been 
brought  entirely  to  rest.  There  is  little  doubt,  however,  that 
the  direction  of  gyratory  motion  is  almost  always,  if  not  en- 
tirely so,  contrary  to  that  of  the  hands  of  a  watch,  though 
reports  are  not  entirely  wanting  of  their  rotation  the  other  way. 

The  direction  of  the  progressive  motion  of  tornadoes  is 
mostly  northeasterly. 

"Of  the  tornadoes  the  courses  of  which  have  been  recorded,  310- 
moved  from  S.W.  to  N.E.;  38  from   N.W.  to  S.E. ;  16  from  W.S.W.  to 
E.N.E.;  14  from  W.  to  E.;  7  from  S.S.W.  to  N.N.E.  ;  5  from  W.N.W. 
to  E.S.E. ;  3  from  N.N.W.  to  S.S.E."     "The  velocity  of  progression  of" 


396  TORNADOES. 

'the  storm  cloud,  as  determined  from  the  reports  in  1 30  cases,  varied  from 
12  to  60  miles,  the  average  being  30.08  miles."73 

The  direction  of  the  general  drift  of  the  air  is  very  nearly 
that  of  the  progressive  motion  of  the  tornado,  and  so  mostly 
from  S.W.  to  N.E.  The  velocity  of  this  is  always  consider- 
able in  comparison  with,  though  generally  much  less  than,  the 
gyratory  velocity  of  the  violent  part  of  the  tornado.  On  the 
right  hand,  and  mostly  the  southeast  side,  of  the  path  of  the 
tornado,  therefore,  the  two  motions  very  nearly  coincide  in 
•direction,  and  so  the  velocity  of  the  resultant  of  the  two  mo- 
tions combined  becomes  much  greater  than  on  the  left-hand 
side  where  the  progressive  and  gyratory  motions  are  somewhat 
in  contrary  directions,  and  where,  consequently,  the  velocity  of 
'the  resultant  motion  is  very  nearly  the  difference  of  the  two 
velocities.  For  this  reason  the  most  violent  and  destructive 
part  of  the  tornado  is  found  on  the  right-hand  side  of  the  cen- 
tral path,  and  the  tornado,  consequently,  as  the  cyclone  (§  202), 
has  its  dangerous  side.  Consequently  where  a  tornado  passes 
through  a  forest  the  fallen  trees  are  found  mostly  on  the  right 
hand  side  of  the  central  track,  and  with  their  tops  in  a  north- 
easterly or  north-northeasterly  direction.  The  gyratory  velo- 
city, however,  may  be  so  great  that  the  weaker  trees  at  least 
are  overthrown  on  the  other  side,  and  then  they  are  there 
found  lying  mostly  in  a  somewhat  contrary  direction. 

260.  On  account  of  the  general  progressive  motion  of  the 
air,  nearly  in  the  direction  of  the  motion  of  the  tornado,  the 
absolute  motion  of  the  air  in  the  front  of  the  tornado  is  nearly 
at  right  angles  to  the  direction  of  the  path,  or  perhaps  gen- 
erally inclines  a  little  forward,  the  progressive  motion  counter- 
acting, and  even  move,  the  inclining  of  the  wind  toward  the 
centre.  But  in  the  rear  of  the  tornado,  the  progressive  motion 
increases  the  inclination  toward  the  centre,  and  here  trees  are 
overthrown  and  objects  carried  nearly  toward  the  centre  and 
in  the  direction  of  the  storm's  path.  The  effect  upon  the 
resultant  direction  is  similar  to  that  in  cyclones,  as  explained 
in  §  201  and  represented  in  Fig.  9.  Where  the  centre  of  a  tor- 
nado passes  over  a  place  in  a  northeasterly  direction  the  trees 


GYRATORY  AND  PROGRESSIVE  MOTIONS.  397 

in  front  may  be  thrown  toward  the  N.  or  N.W.,  but  in  the  rear 
toward  the  E.,  or  still  more  around  toward  the  N.E.  in  the  direc- 
tion of  the  storm's  progress.  In  consequence  of  the  progressive 
motion  in  the  rear  of  a  tornado  being  more  nearly  in  the  direc- 
tion of  the  gyratory  motion,  the  winds  in  the  rear  are  usually 
stronger  than  in  the  front  part,  and  so  the  stronger  trees,  which 
are  not  overthrown  in  the  former,  may  be  prostrated  in  the 
latter. 

Where  the  right-hand  side  of  a  tornado  passes  over  a  place 
the  trees  may  be  first  thrown  toward  the  N.W.  or  N.,  but 
mostly  by  the  south  quadrant  of  the  tornado  toward  the  N.E., 
for  here  the  gyratory  and  progressive  motions  most  nearly 
coincide  in  directions,  and  consequently  the  resultant  velocities 
are  the  greatest :  and  this  is  the  most  dangerous  part  of  a  storm. 
But  if  the  left-hand  side  pass  over  a  place,  the  trees  may  be 
thrown  successively  toward  the  N.W.,  W.,  and  S.W.,  and  by 
the  western  quadrant  even  toward  the  S.  or  S.E.  Hence  it  is 
stated  with  regard  to  the  Gentry  County  tornado  :72 

"The  largest  trees  were  twisted  off  near  the  ground,  uprooted,  or 
broken  off,  and  lay  with  their  tops  pointing  in  a  circular  direction  from 
right  to  left  within  the  central  part  of  greatest  destruction.  Those  on 
the  S.  (right-hand)  side  of  the  centre  were  pointing  to  the  E.  and  N.E., 
and  even  N.W.  when  very  near  the  centre.  On  the  N.  side  they  were 
pointing  N.W.,  W.,  S.W./and  S.E." 

261.  In  the  progression  of  a  tornado  in  a  northeasterly  di- 
rection, the  trees  first  thrown  down  being  those  of  the  front 
part,  are  thrown  more  from  an  easterly  direction  than  those 
afterward  prostrated  by  the  rear  part,  which  are  decidedly 
from  a  westerly  direction,  because  here  the  progressive  and 
gyratory  motions  are  somewhat  in  the  same  direction.  Those 
from  a  more  easterly  direction,  therefore,  where  they  cross, 
generally  lie  under  those  of  a  more  westerly  direction.  This 
accords  with  the  observations  of  Dr.  Anderson,68  who  says : 

"  The  first  area  examined,  tornado  of  April  23,  1883,  was  composed  of 
two  distinct  parts.  The  first  was  a  long  rectangular  space  of  about  half 
a  mile  in  length,  from  west-southwest  to  east-northeast,  and  a  hundred 
and  fifty  to  two  hundred  yards  in  width.  Within  this  space  the  trees- 
were  prostrated  from  southeast,  south,  southwest,  and  west,  and  inter- 


TORNADOES. 

mediate  points ;  and  wherever  two  were  found  lying  across  each  other, 
the  one  thrown  from  the  direction  the  nearest  to  east,  or  farthest  around 
from  west,  was  always  at  the  bottom.  Thus,  those  thrown  from  south 
always  lay  on  top  of  those  from  southeast,  those  from  west  were  always 
on  top  of  all  other  directions.  This  order  was  without  exception.  The 
rectangular  area  terminated  at  the  east  end  in  an  irregularly  circular  area 
of  about  eight  hundred  yards  diameter,  either  east  and  west  or  north  and 
south.  Bisecting  this  area  both  ways  and  dividing  it  into  four  quad- 
rants, the  southwest  and  southeast  were  found  to  correspond  in  all  re- 
spects with  the  rectangular  area,  except  that  in  the  southeast  there  was 
a  greater  proportion  of  trees  thrown  down  from  east-southeast  and 
southeast  than  in  the  other  sections ;  and  in  the  southwest  quadrant, 
near  the  centre,  a  tree  thrown  from  the  southwest  was  overlaid  by  one 
from  south,  the  single  exception  to  the  order  noted  above.  In  the  north- 
east quadrant  the  destruction  was  less  than  in  either  of  the  others,  and 
trees  were  thrown  down  from  east,  northeast,  north,  northwest,  and 
west.  In  the  northwest  quadrant  the  trees  were  thrown  from  north, 
northwest,  and  west,  chiefly  from  northwest,  west-northwest,  and  west ; 
•and  in  the  instances  where  they  crossed  each  other,  the  order  in  relation 
to  the  west  was  similar  precisely  to  that  of  the  other  parts,  progressing 
irom  east  round  by  north  to  west,  as,  on  the  other  side,  the  progression 
was  from  east  round  by  south  to  west ;  so  that  in  these,  the  northeast 
•and  northwest  quadrants,  trees  thrown  from  northeast  lay  under  those 
from  north,  those  from  north  under  those  from  northwest,  while,  as  in 
the  south  quadrants  and  the  rectangular  space,  those  from  west  were  on 
top  of  all." 

The  destruction  and  prostration  of  trees  in  the  rectangular 
;area  referred  to  was  caused  by  the  dangerous  side  while  the 
tornado  had  a  progressive  motion,  the  other  side  not  having 
.sufficient  violence  to  prostrate  the  trees.  But  at  the  end  of 
this  area  the  tornado  seems  to  have  remained  nearly  stationary 
for  £  short  time,  when  the  violence  was  nearly  the  same  on 
both  sides,  and  during  this  time  trees  were  prostrated  on  the 
nor,th  side,  in  the  northeast  and  northwest  quadrants.  The 
•order  of  prostration  in  the  rectangular  strip,  and  in  the  south- 
east and  southwest  quadrants  while  the  tornado  was  stationary, 
was  the  same  from  east  around  by  south  to  the  southwest, 
while  in  the  northeast  and  northwest  quadrants,  while  the  tor- 
nado was  stationary,  the  order  was  the  reverse,  from  the  east 
round  by  north  to  west. 


RAINFALL   IN   TORNADOES.  399 

On  account  of  the  right-hand  side  of  a  tornado,  as  already 
-explained,  being  the  more  violent  and  destructive  side,  there  is 
generally  a  marked  difference  in  the  width  of  the  destructive 
parts  of  the  two  sides.  With  regard  to  this  it  is  stated  in  the 
account  of  the  Lees  Summit  tornado  : 73 

"  Mr.  Bradley  and  his  son,  who  had  been  engaged  for  several  days  in 
putting  up  fences  over  the  path  of  the  storm,  were  struck  with  the 
marked  contrast  in  the  comparative  width  of  the  E.  and  W.  sides  of  the 
-storm's  track.  For  a  distance  of  nearly  four  miles  they  had  found  that 
the  W.  (left-hand)  side  averaged  about  40  rods  in  width,  the  maximum 
being  80  and  the  minimum  25  rods.  On  the  E.  (right-hand)  side,  over 
the  same  distance,  the  average  width  was  over  a  mile,  the  maximum  be- 
ing two  miles  and  the  minimum  three  fourths  of  a  mile." 

Finley  also  states  with  regard  to  the  tornado  tracks  gener- 
-ally : 72 

"  The  left  or  W.  side  was  always  the  narrowest,  and,  unless  within  the 
limits  of  the  path  of  greatest  destruction,  the  force  manifested  was  al- 
ways the  weakest  on  this  side.  I  inquired  repeatedly  if  any  one  experi- 
•enced  strong  inrushing  currents  on  this  side  which  were  often  mentioned 
-as  occurring  on  the  opposite  side,  but  always  received  a  negative  answer. 
The  W.  side  was  generally  from  one  third  to  one  half  as  wide  as  the  E. 
:side  or  right-hand  side." 

In  the  tornado  investigated  by  Dr.  Anderson,  while  it  had 
•a  rapid  progressive  motion,  the  left-hand  side  of  the  destruc- 
tive part  seems  to  have  been  entirely  wanting,  so  far  as  the 
prostration  of  trees,  at  least,  is  concerned. 

RAINFALL   IN  TORNADOES. 

262.  The  rapid  ascent  of  nearly  saturated  air  in  a  tornado 
must  give  rise  generally  to  a  great  amount  of  rainfall.  Some 
idea  of  this  may  be  formed  from  considering  the  amount  of 
aqueous  vapor  in  the  ascending  air,  drawn  mostly  from  the 
strata  near  the  earth's  surface,  and  its  capacity  for  vapor,  from 
which  the  amount  left  in  the  air,  after  it  has  ascended  up  to 
altitudes  where  it  has  become  cooled  down  to  a  lower  temper- 
ature, becomes  known.  Suppose  the  air  temperature  near  the 
earth's  surface  is  25°  C,  but  that  the  depression  of  the 


4OO  TORNADOES. 

point  is  5°.  The  tension  of  aqueous  vapor  in  the  air,  in  milli- 
meters of  mercury,  is  that  of  saturation  at  20°;  and  with  this 
as  an  argument  Table  n  gives  17.36  mm.  The  density  of 
vapor  being  0.622,  this  gives  17.36  X  0.622  =  10.80  mm.  for  the 
height  of  a  column  of  mercury  equal  to  the  weight  of  aqueous 
vapor  in  a  homogeneous  atmosphere  of  saturated  air  at  the 
temperature  of  20°.  Multiplying  this  by  13.6,  the  density  of 
mercury,  we  get  10.80  X  13.6=  146.7  mm.  for  the  height  of 
a  corresponding  column  of  water.  Dividing  this  by  7992,. 
the  height  in  meters  of  a  homogeneous  atmosphere,  we  get 
0.0184  mm.  for  the  depth  of  rain  in  each  stratum  of  saturated 
atmosphere  of  one  meter  in  depth,  and  of  the  temperature  of 
20°  if  the  vapor  were  all  precipitated.  If  now  we  suppose  that 
the  ascending  velocity  of  the  air  at  the  base  of  the  cloud  where 
condensation  first  commences  to  be  60  meters  per  second,  then 
the  depth  of  rainfall,  supposing  the  current  to  extend  so  high 
that  all  the  vapor  is  coudensed,  and  that  the  rain  all  falls  di- 
rectly back,  would  be  0.0184  X  60  =  i.i  mm.  per  second,  or 
0.066  m.  (about  2.6  inches)  per  minute.  With  higher  temper- 
atures and  higher  degrees  of  saturation  the  rate  of  rainfall 
would  be  considerably  more. 

The  preceding  calculation,  however,  upon  the  assumptions 
made,  gives  us  only  a  rough  approximate  idea  of  the  possible 
rate  of  rainfall,  for  the  air,  at  least  all  of  it,  never  ascends  so 
high  that  all  the  vapor  is  condensed ;  but,  on  the  contrary,  as 
has  been  explained  in  §  241,  the  ascending  current  may  be  de- 
flected off  laterally  on  all  sides  at  no  very  great  altitude.  The 
vapor,  therefore,  which  is  carried  up  mostly  by  the  more  rapid 
currents  in  the  interior  of  the  tornado  after  being  condensed 
into  rain,  is  carried  outward  above  by  the  outflowing  currents 
there,  and  falls  mostly  over  the  regions  adjacent  to  the  vio- 
lent part  of  the  tornado,  and  not  directly  back  over  the  place 
where  it  ascended  as  vapor.  Besides,  we  have  just  seen  that 
where  there  is  an  ascending  current  of  only  moderate  velocity, 
small  rain-drops  cannot  fall  back,  but  are  carried  up  to  where 
the  current  is  outward,  and  then  out  where  there  is  little  or  no. 
ascending  current,  and  where  they  are  permitted  to  fall  to  the 


WATERSPOUTS. 


401 


earth.  In  fact,  with  an  ascending  velocity  even  very  much  less 
than  that  assumed  above,  no  ordinary  rain-drops  by  Table  VII 
could  fall  directly  back  to  the  earth. 


WATERSPOUTS. 

263.  As  soon  as  the  ascending  and  expanding  air  in  a  tor- 
nado cools  down  to  the  dew-point  corresponding  to  the  di- 
minished vapor  tension  as  it  gradually  comes  under  less  pres- 
sure, condensation  and  cloud  formation  take  place.  Where 
the  air  ascends  vertically,  we  have  seen,  §  27,  this  takes  place 
at  an  altitude  which,  in  meters,  is  equal  very  nearly  to  the  de- 
pression of  the  dew-point  at  the  earth's  surface  in  centigrade 
degrees  multiplied  by  125  or  125  (r  —  d\ 

But  the  rate  of  cooling  does  not  necessarily  depend  upon 
the  ascent  of  vapor,  but  only  on  the  amount  of  decrease  of 
pressure  and  of  expansion,  whether  this  takes  place  in  the  ascent 
or  horizontal  motion  of  air,  or  in  air  without  any  motion.  In 
all  cases,  to  a  given  amount  of  decrease  of  pressure  and  corre- 
sponding increase  of  expansion  there  is  a  corresponding  de- 
crease of  temperature. 

If  in  the  annexed  figure  we  suppose  that  the  horizontal  iso- 
baric  surface  in  the  undisturbed  air,  and  represented  by  a  hori- 


Fig.  3. 

zontal  line  ab,  is  brought  down  by  tornadic  action  to  the  earth's 
surface  DE  at  /  in  the  form  of  the  line  af,  as  explained  in 
§  233,  then  the  air  which  ascends  from  the  stratum  next  to 


4O2  TORNADOES. 

the  earth's  surface,  all  supposed  to  have  the  same  temperature 
and  dew-point,  whether  it  ascends  slowly  and  nearly  vertically 
at  the  outer  border  as  at  a  and  b,  or  more  obliquely  and  rapidly 
toward  and  up  in  the  interior,  wherever  it  arrives  at  the  de- 
pressed isobaric  surface,  represented  by  the  curved  line  af  or  bft 
it  has  cooled  down  to  the  same  temperature  ;  and  if  the  height  of 
that  isobaric  surface  before  being  depressed  in  the  interior  of 
the  tornado  was  125  (r  —  d],  then  condensation  and  cloud  for- 
mation take  place  as  soon  as  the  air  ascends  above  or  enters 
within  that  surface  up  as  high  as  aqueous  vapor  is  carried  by 
the  ascending  current.  But  without  and  below  this  surface 
there  is  no  condensation  and  cloud  formation,  and  the  air  re- 
mains unclouded.  The  clouded  portion  of  the  air  therefore 
assumes  the  form  of  a  tapering  trunk,  as  outlined  on  the  two 
sides  by  the  curved  lines  bf  in  the  figure,  and  we  have  the 
phenomenon  called  a  waterspout.  A  waterspout,  therefore,  is 
simply  the  cloud  brought  down  to  the  earths  surface  by  the  rapid 
gyratory  motion  of  the  tornado.  As  Espy  with  a  few  strokes 
of  the  handle  of  an  air-pump  produced  a  cloud  in  the  receiver 
from  the  expansion  and  cooling  of  the  moist  air  within,  so  na- 
ture, by  means  of  a  whirl  in  the  open  atmosphere,  produces  a 
cloud  in  the  vortex  of  a  tornado,  from  the  expansion  and  cool- 
ing of  the  air  there,  on  account  of  the  partial  vacuum  caused  by 
the  centrifugal  force  of  the  gyrations. 

We  have  seen,  §  242,  that  the  air  which  ascends  in  the  in- 
terior of  a  tornado  comes  in  below  mostly  near  the  earth's  sur- 
face— especially  that  which  ascends  where  the  spout  is  formed, 
and  so  it  may  be  regarded  as  all  having  very  nearly  the  same 
temperature  and  depression  of  the  dew-point.  If  the  compara- 
tively small  amount  of  air  coming  in  at  the  sides  from  the 
higher  strata  of  the  atmosphere  had  the  same  depression  of  the 
dew-point,  it  would  have  to  enter  some  distance  within  the  iso- 
baric surface  af,  ^/"before  condensation  of  the  vapor  would  com- 
mence, since  having  a  less  pressure  before  commencing  to 
ascend  than  at  the  earth's  surface,  it  would  have  to,  arrive  when 
the  pressure  is  less  than  that  of  the  isobaric  surface  of  incipient 
condensation  for  air  ascending  from  the  earth's  surface,  and  so 


WATERSPOUTS.  403 

the  outline  of  the  spout  is  determined  by  the  latter.  If,  how- 
ever, the  air  entering  from  the  higher  strata  should  have  a  much 
less  depression  of  the  dew-point,  its  vapor  might  begin  to  be 
condensed  before  entering  within  and  above  this  surface,  and 
so  affect  the  distinctness  of  outline  of  the  spout ;  but  this  can 
scarcely,  if  ever,  occur,  since  the  further  from  the  earth's  sur- 
face, generally,  the  drier  the  undisturbed  quiet  air. 

The  arrows  in  the  figure  represent  approximately  the  air 
currents  coming  in  from  the  sides,  and  mostly  near  the  earth's 
surface,  to  supply  the  draught  of  the  rapidly-ascending  current  in 
the  interior.  It  must  be  understood,  however,  that  these  repre- 
sent merely  the  currents  of  the  vertical  circulation,  and  that  in 
a  tornado  there  is,  in  connection  with  this,  also  a  rapid  gyra- 
tory motion  around  the  centre.  The  same  system  of  circula- 
tion somewhat  takes  place  in  all  tornadoes,  whether  the  tor- 
nadic  violence  is  sufficient  to  bring  down  the  spout  or  not ;  for, 
as  will  be  explained,  a  certain  degree  of  violence  is  necessary 
to  bring  the  spout  down  to  the  earth's  surface.  At  a  consider- 
able distance  from  the  centre,  beyond  the  limits  represented  by 
the  figure,  the  air  on  all  sides  descends,  mostly  very  gently,  and 
at  the  same  time  is  drawn  in  toward  the  interior. 

264.  The  height  of  the  spout  depends  upon  the  hygro- 
metric  state  of  the  air,  being  125  meters  for  each  degree  of  the 
depression  of  the  dew-point  at  the  earth's  surface.  The  diame- 
ter of  the  spout  at  any  given  distance  /  below  the  level  of  the 
undisturbed  isobaric  surface  AJ3,  as  at  a  or  ft  Fig.  I,  §  233,  de- 
pends upon  the  amount  of  gyratory  velocity  or  value  of  c  =  r'v', 
as  may  be  seen  in  §  234 ;  for  the  greater  the  value  of  c,  the 
greater  is  the  value  of  r  the  distance  of  the  isobaric  surface 
from  the  centre,  and,  in  the  case  of  a  waterspout,  the  greater  is 
its  radius.  Since  the  spout  is  tapering  down  to  the  earth's  sur- 
face, the  drier  the  air  and  the  taller  the  spout  the  smaller  its 
diameter  at  the  earth's  surface  for  the  same  gyratory  velocities. 
For  instance,  with  a  small  dew-point  depression  and  rapid 
gyratory  motion  we  get  a  spout  of  the  form  of  Fig.  4  in  which 
the  cloud  is  low  on  the  outer  border  of  the  tornado  where  the 
isobaric  surface,  or  surface  of  incipient  condensation,  is  not  de- 


404 


TORNADOES. 


pressed  sensibly,  and  on  account  of  the  smallness  of  the  de- 
pression /  and  the  largeness  of  the  value  of  r'v',  the  value  of  r 
is  large,  as  is  seen  from  the  inspection  of  the  equation  of  §  234. 
With  the  conditions  there  assumed  of  r'v'  =  3000,  and  /  =  500 
meters,  which  corresponds  to  a  depression  of  the  dew-point  of 
4°,  we  get  for  the  radius  of  the  spout  at  the  earth's  surface,. 


Fig.  4. 


Fig.  5. 

r  =  30  meters,  and  hence  a  short  spout  only  500  meters  in 
height  with  a  diameter  of  60  meters  at  the  base.  In  a  tornado 
under  such  conditions  even  the  cloud-rim  is  low,  and  the  dense 
cloud  is  brought  down  to  the  earth's  surface  over  a  considerable 
area  at  any  given  instant,  and  everything  is  involved,  for  the 
time,  in  great  darkness. 

On  the  other  hand,  if  the  air  is  very  dry  and  the  depression, 


WATERSPOUTS. 


405 


consequently,  of  the  dew-point  very  great,  we  get  a  very  tall 
spout  with  small  diameter,  as  represented  in  Fig.  5.  If  the  de- 
pression of  the  dew-point  is  16°  C,  then  the  height  of  the  spout 
is  1 25  X  1 6  =  2000  meters ;  and  if  in  this  case  we  put  r'v'  =  1000, 
we  get  from  the  expression  of  /,  §  234,  by  putting  /  =  2000 
meters,  as  above  assumed,  r  =  5  meters  nearly,  or  a  diameter 
of  about  10  meters  for  the  spout  at  the  earth's  surface.  But 
the  value  of  r'v'  cannot  be  taken  so  small,  or  that  of  /  so  great, 
that  r  vanishes,  so  that  in  any  case  there  must  be  at  least  a  small 
threadlike  spout  coming  down  to  the  ground  according  to  the 
theory,  in  which  we  take  n'o  account  of  friction. 

265.  In  the  preceding  results  from  theory  and  formulae  in 
which  no  account  is  taken  of  friction,  of  course  considerable 


s  f 

Fig.  6. 

allowance  must  be  made  for  its  effect,  as  has  heretofore  been 
pointed  out  in  similar  cases.  It  has  been  shown  that  the  greater 
the  initial  gyratory  velocity  or  value  of  r'v'  =  c,  the  greater 
the  diameter  of  the  spout,  all  other  circumstances  being  the 
same.  Consequently  the  effect  of  friction,  which  tends  to  di- 
minish the  gyratory  velocity,  is  to  make  the  diameter  of  the 
spout  smaller,  and  even  to  vanish  where  the  gyratory  velocity 
is  small ;  and  this  is  especially  the  case  very  near  the  earth's 
surface  where  the  amount  of  friction  and  decrease  of  gyratory 


406 


TORNADOES. 


velocity  are  comparatively  great.  For  instance,  if  we  had  con- 
ditions which  would  give  a  theoretical  spout  of  the  form  out- 
lined by  the  dotted  curved  lines  bf,  Fig.  6,  the  effect  of  friction 
would  diminish  its  diameter  somewhat  as  represented  in  the 
figure,  and  even  prevent  its  coming  entirely  down  to  the  earth's 
surface. 

With  a  still  less  gyratory  velocity,  other  conditions  remain- 
ing the  same,  there  would  simply  be  a  funnel-shaped  cloud  as 
represented  in  Fig.  7,  the  gyrations  in  this  case  retarded  by 
friction,  being  merely  sufficient  to  bring  the  cloud  in  the  vortex 
a  little  below  the  general  level  of  the  undisturbed  base  of  the 


Fig.    7. 

cloud.  It  is  in  this  form  it  first  appears  in  a  tornado,  when  it 
is  seen  at  all ;  and  as  the  energy  of  the  tornado  and  the  veloci- 
ty of  the  gyrations  increase,  it  may  be  brought  either  wholly 
or  only  part  of  the  way  down  to  the  earth's  surface.  Finally, 
as  the  energy  of  the  tornado  becomes  exhausted,  and  the 
velocity  of  the  gyrations  diminishes,  it  is  drawn  up  again  ap- 
parently into  the  cloud,  its  last  appearance  being  again  that  of 
the  funnel-shaped  cloud. 

In  tornadoes  of  large  base  with  not  fully  developed  and 
rapid  gyratory  velocities  in  the  vortex,  instead  of  a  completely 
developed  spout  or  a  funnel-shaped  cloud,  a  large  basket- 
shaped  cloud  is  observed  suspended  from  the  level  of  the  gen- 
eral base  of  the  clouds.  The  rapidity  of  the  gyratory  veloci- 
ties in  the  vortex  is  not  sufficient  to  bring  the  cloud  down 
with  a  sharp  point  as  in  the  funnel-shaped  cloud. 

The   action   of  a  tornado   is   somewhat   intermittent,  now 


WA  TERSPO  UTS.  407 

stronger  and  again  weaker.     This  is  observed  frequently  in  the 
greater  manifestation  of  violence  at  some  times  than  at  others. 
With  regard  to   the  tornado   force  in  the  S.  C.  tornadoes 
of  April,  1883,  Dr.  Anderson  states:68 

"  The  tracks  examined  by  me  did  not  present  continuous  lines  of  de- 
struction, but  areas  of  destruction  separated  by  intervals  entirely  or  al- 
most entirely  exempt  from  destructive  forces  ;  from  which  it  is  inferred 
that,  while  the  storm,  in  its  common,  ordinary  features,  pursued  its  way 
steadily  onward  by  bodily  transference,  the  tornadic  action  was  devel- 
oped interruptedly,  and  progressed  by  successive  transplantings." 

That  is  to  say,  in  the  general  progress  of  the  tornado,  the 
unstable  state  and  the  vertical  circulation  continues  nearly  the 
same,  but  the  gyratory  motion  depends  very  much  upon  the 
initial  and  slight  whirl  which  the  air  near  the  earth's  surface  at 
some  distance  from  the  centre  may  have,  as  it  is  drawn  into 
and  up  the  vortex ;  for  while  the  whirling  column  above  con- 
sists somewhat  of  the  same  air  drifting  along,  that  near  the 
surface,  not  partaking  of  the  same  amount  of  progressive  veloci- 
ty, is  being  continually  changed,  and  consequently  the  value 
of  c  =  r'v' ,  upon  which  the  gyratory  motion  depends  (§  232.) 
According  as  the  value  of  c  is  greater  or  less,  for  the  new  por- 
tions of  air  drawn  into  the  central  part,  is  the  gyratory  velocity 
and  violence  of  the  tornado  greater  or  less.  This  intermittent 
action  in  tornadoes  is  often  indicated  by  the  dropping  down 
and  rising  up  of  the  spout  where  the  gyratory  violence  of  the 
tornado  is  barely  sufficient  to  develop  a  spout,  and  is  an  ex- 
planation of  this  phenomenon  ;  for  in  that  case  a  very  little  in- 
crease or  decrease  in  the  rapidity  of  the  gyrations  brings  the 
spout  in  part  or  wholly  to  the  earth's  surface  from  the  funnel 
shape,  or  lets  it  up  again. 

Finley  states,  with  regard  to  the  Lee's  Summit  tornado,  that 
from  a  certain  point  "the  funnel  raised  again,  committing  no 
damage  for  a  distance  of  9!  miles  over  an  alternation  of  hill 
and  dale,  when  it  struck  a  large  elm-tree  situated  in  a  broad 
valley  with  gently  sloping  sides."  While  passing  over  the  un- 
even surface  of  hill  and  dale,  the  gyratory  violence,  on  account 
of  this  unevenness,  was  not  sufficient  to  keep  the  spout  down 
to  the  earth's  surface,  and  so  here  it  rose  up. 


4O8  TORNADOES. 

In  the  account  of  the  Walterborough  tornado,69  it  is  stated 
that  "its  path  was  continuous  for  24  miles,  then  a  gap  of  25 
miles  where  no  damage  was  done,  followed  by  a  track  f  mile 
in  length/' 

With  increase  of  tornadic  violence,  the  spout  is  brought 
down  to  the  earth,  and  the  consequent  increased  destructive- 
ness  is  attributed  to  the  spout,  whereas  the  latter  is  simply  an 
effect  of  the  increase  of  the  tornadic  violence,  and  with  a  drier 
air  there  might  be  no  spout  accompanying  the  same  amount  of 
violence  and  destructiveness. 

266.  From  what  precedes,  it  is  evident  that  waterspouts 
may  be  of  a  great  variety  of  forms,  varying  from  that  of  a 
cloud  brought  down  over  a  large  area  of  the  earth's  surface  in 
a  tornado,  where  the  air  is  nearly  saturated  with  vapor  and 
the  general  base  of  the  clouds  very  low,  somewhat  as  repre- 
sented in  Fig.  4,  to  that  which  occurs  when  the  air  is  very  dry, 
and  when  the  tornadic  action  is  barely  able  to  bring  the  cloud 
down  from  a  great  height  into  a  slender  spout  of  small  diame- 
ter, somewhat  as  represented  in  Fig.  5.  Horner  says  that  their 
diameters  range  from  2  to  200  feet  and  their  heights  from  30 
to  1 500  feet.  Dr.  Reye  states  that  their  diameters  on  land,  at 
base,  are  sometimes  more  than  1000  feet.  Oersted  puts  the 
usual  height  of  watesprouts  from  1500  feet  to  2000  feet,  but 
states  that  in  some  rare  cases  they  cannot  be  much  less  than 
5000  or  6000  feet.  On  the  I4th  of  August,  1847,  Professor 
Loomis  observed  a  waterspout  on  Lake  Erie,  the  height  of 
which,  by  a  rough  estimate,  was  a  half  a  mile,  and  the  diame- 
ter about  10  rods  at  the  base  and  20  rods  above.74 

Judge  Williams,  in  speaking  of  the  tornado  of  Lee's  Sum- 
mit, where  he  saw  it,  says  :72  "  It  seemed  to  be  about  the  size 
of  a  man's  body  where  it  touched  the  clouds  above,  and  then 
tapered  down  to  the  size  of  a  mere  rod." 

The  preceding  symmetrical  waterspouts,  deduced  from  the- 
ory upon  certain  assumed  regular  conditions,  differ  of  course 
very  much  in  form  from  those  usually  observed  in  nature, 
where  these  regular  conditions  are  rarely  found,  even  approxi- 
mately. It  is  assumed  in  the  theory  that  the  progressive  mo- 


WATERSPOUTS. 

tion  of  the  strata  of  the  atmosphere  at  all  heights  to  which  the 
tornado  extends  is  the  same,  from  which  results  a  perfectly 
straight  and  vertical  spout.  But  this  condition  usually  does 
not  exist,  but  the  upper  strata  either  move  faster  or  slower 
than  the  lower  ones,  and  so  in  the  former  case  the  upper  part 
of  the  spout  inclines  forward  and  in  the  latter  backward. 
Sometimes  the  progressive  motions  of  the  atmosphere  in  the 
different  strata  are  not  only  very  irregular  at  different  alti- 
tudes, on  account  of  the  great  abnormal  disturbances  to  which 
the  winds  are  subject,  but  likewise  very  changeable  at  different 
times,  so  that  in  this  case  the  spout  may  not  only  be  bent  and 
sinuous,  but  subject  to  continual  contortions  and  twistings. 
Hence,  the  Rev.  S.  R.  Reese  describes  the  appearance  of  the 
spout  of  the  Lee's  Summit  tornado,  as  he  saw  it,72  to  be  "  that 
of  a  funnel,  at  times  elongated  in  a  serpentine-like  form  of 
heavy  mould,  hung  up  by  the  head  and  writhing  in  agony,  its 
tail  curling  and  lashing  as  if  actuated  by  the  impulses  of  a  liv- 
ing body.  It  was  above  the  ground  and  doing  no  damage, 
though  at  times,  in  its  violent  contortions  and  struggles,  it 
•would  descend  very  near  the  ground." 

Other  irregularities  arise,  also,  from  unequal  distributions  of 
temperature  and  of  aqueous  vapor  in  all  portions  of  the  air 
around  on  all  sides.  The  base  of  the  cloud  also,  from  which 
the  spout  depends,  does  not  have  the  smoothness  and  the  uni- 
formity on  all  sides  shown  in  the  preceding  graphic  representa- 
tions of  the  results  deduced  from  theory.  For  although  the 
surface  of  incipient  condensation,  as  the  air,  charged  with 
vapor,  ascends,  may  be  somewhat  regular,  yet  the  cloud  above 
is  at  some  distance  from  the  vortex  brought  down  below  this 
level  in  the  form  of  scud  clouds,  which  often  gives  it  an  irregu- 
lar and  jagged  appearance.  In  fact,  this  regular  base  of  in- 
cipient condensation  and  the  extreme  upper  wide  part  of  the 
spout  or  funnel  is  frequently  concealed  by  such  clouds,  which 
.are  brought  down  and,  before  they  are  evaporated,  are  carried 
into  the  vortex.  For  although  the  air  is  drawn  into  the  vor- 
tex below,  at  the  earth's  surface  mostly,  as  has  been  explained, 
yet  it  also  seems  to  be  drawn  down  also,  at  no  great  distance 


410  TORNADOES. 

from  the  vortex,  to  supply  the  ascending  current ;  and  so  it 
brings  portions  of  the  cloud  above  down,  sometimes  even  near 
to  the  earth's  surface.  Thus,  in  the  Lee  Summit  tornado,72 

"  The  funnel  is  represented  as  reaching  the  ground,  which  under  such 
circumstances  causes  the  narrowest  part  to  be  some  distance  above  the 
surface,  but  when  it  rises  the  lower  portion  tapers  down  to  a  very  small 
diameter.  Dark  masses  of  cloud  shot  downward  on  either  side  of  the 
funnel,  entering  it  just  above  the  ground,  apparently  thereafter  rushing, 
upward  through  the  centre." 

Espy  says: 

"  Whenever  low  clouds  appear  under  the  rim  of  the  hurricane  cloud, 
they  always  are  seen  in  the  form  of  scud  moving  rapidly  toward  the 
centre  of  the  great  hurricane  cloud,  where  they  unite  with  its  base  and 
ascend  with  the  ascending  current,  where  the  barometer  is  very  low." 

267.  Waterspouts,  especially  on  land,  frequently  have  the: 
appearance  of  a  widening  at  the  bottom  on  the  earth's  surface. 
On  land,  dust  and  a  great  many  light  substances  are  carried  up 
in  the  interior  ;  and  as  they  are  being  collected  from  all  sides 
on  the  earth's  surface  by  the  inflowing  currents,  which  are 
here  more  nearly  radial,  toward  the  vortex  below,  they  often 
assume  the  form  of  a  cone,  which,  in  the  first  formation  of  the 
spout,  seems  to  rise  up  and  meet  the  descending  spout  falling 
apparently  from  the  clouds,  and  thus  the  whole  phenomenon 
often  assumes  the  form  of  an  hour-glass.  Of  the  great  tornado* 
of  West  Cambridge  (now  Arlington),  August  22,  1851,  it  was 
said  : 

"  To  some  who  watched  it  closely  its  form  resembled  a  tall,  wide- 
spreading  elm  tree.  To  others  it  appeared  like  an  inverted  cone.. 
Several  represented  it  as  a  dense  upright  column,  and  a  few  as  having 
the  shape  of  an  hour-glass." 

The  several  observers  no  doubt  saw  it  at  different  times- 
and  under  somewhat  different  circumstances  in  its  progressive 
motion  over  the  inequalities  of  surface.  It  was  only  where  the 
earth  contained  a  great  amount  of  dust,  or  other  light  materials 
on  the  surface,  that  the  right  cone  at  the  base  was  observed,, 
and  where  the  whole  assumed  the  form  of  an  hour-glass. 


WATERSPOUTS. 


411. 


With  regard  to  the  Lee's  Summit  tornado,  it  was  stated :" 

"  The  small  funnel  cloud  was  seen  reaching  part  way  to  the  ground; 
at  the  same  time  an  inverted  funnel  of  dust  and  light  materials  formed 
over  the  earth  beneath  and  reached  up  to  it." 

The  graphic  representation  of  it  in  Fig.  8  is  given  in  the 
account  of  it. 

Sometimes  the  right  and  inverted  cones  do  not  come  to- 
gether, but  a  small  space  is  left  between  the  two  vertices  of  the- 


Fig.  8. 


Fig.  9. 

cones,  pointing  the  one  down  and  the  other  up  toward  each 
other.  From  no  accounts  can  it  be  inferred  that  in  land  torna- 
does the  lower  part  is  composed  of  condensed  vapor — at  least 
the  outer  part  of  it,  which  causes  the  widening,  but  the  true, 
spout  may  reach  through  it  to  the  earth's  surface. 


412 


TORNADOES. 


There  are  often  two  or  more  spouts  in  close  proximity. 
The  graphic  representation  in  Fig.  9  of  two  spouts,  brought 
part  of  the  way  down  to  the  earth,  seen  by  Mrs.  Kerr  in  the 
Lee's  Summit  tornado,  is  given  by  Finley.  Sometimes  several 
small  spouts  protrude  from  the  lower  base  of  the  cloud  in  the 
same  vicinity,  some  to  a  greater  and  some  to  a  less  distance 
down,  sometimes  not  differing  much  in  size  ;  at  others  there  is 
a  larger  and  principal  spout  accompanied  by  one  or  more 
smaller  ones.  The  accompanying  representation  of  a  group  of 
little  spouts  or  funnels,  as  seen  by  McLaren  at  one  time  in  the 
JDelphos  tornado,  is  given  by  Finley. 


Fig.  10, 

As  the  tornado  originates  in  air  in  the  unstable  state,  it 
»often  happens  that  there  is  about  an  equal  tendency  in  the  air 
of  the  lower  stratum  to  burst  up  through  those  above  at  several 
places  in  the  same  vicinity  at  the  same  time.  Each  of  these 
gives  rise  to  a  separate  and  independent  gyration  in  the  atmos- 
phere, and  a  small  funnel  where  they  are  of  sufficient  violence  ; 
but  generally,  as  they  increase  in  dimensions  and  violence, 
they  interfere  with  one  another  and  finally  become  united  into 
one.  This  seems  to  have  been  the  case  in  the  tornado  of  St. 
Cloud  and  Sauk  Rapids,  in  the  formation  of  which  it  is  stated 
that  as  the  clouds  began  to  revolve  sharp  points  suddenly  shot 
downward.  As  in  cyclones  there  are  generally  smaller  second- 
ary ones  included,  complicating  the  resultant  motions  of  the 
*air  and  causing  irregularities  in  the  isobars,  so  in  tornadoes 


WATERSPOUTS.  413 

there  are  undoubtedly  secondary  whirls  independent  of  the 
main  one,  though  not  always  accompanied  by  corresponding^ 
funnel  clouds  visible  above.  This  seems  to  be  indicated  by 
side-or  spur  tracks  sometimes  observed  in  connection  with  the 
main  track,  and  by  isolated  spots  at  some  distance  from  the 
main  track  "with  every  tree  uprooted  and  piled  in  confusion."8 

268.  Waterspouts  at  sea  are  usually  more  regular  and 
better  defined  than  those  on  land,  and  the  whole  area  of 
tornadic  disturbance  is  generally  smaller,  so  that  the  spouts 
may  be  approached  with  safety  within  a  very  short  distance, 
and  it  is  only  the  larger  and  more  violent  ones  that  seriously- 
injure  a  ship  running  into  them.  The  destructive  gyratory 
winds,  even  in  the  larger  ones,  extend  only  a  short  distance 
from  the  centre,  and  at  distances  a  little  greater  scarcely  a 
breeze  sometimes  is  experienced.  The  reason  of  this  is  that, 
the  surface  of  the  sea  being  smoother  than  that  of  the  land,, 
there  is  a  more  nearly  perfect  development  of  the  gyrations,, 
and  a  greater  concentration  of  energy  in  the  centre  of  the 
vortex,  although  the  whole  amount  of  energy  is  generally 
smaller  on  sea  than  on  land,  since  this  arises  from  the  unstable 
state,  which  is  more  liable  to  occur,  and  to  a  greater  degree  of 
unstability,  on  land,  where  the  surface  of  the  earth  becomes 
much  warmer  than  that  of  the  ocean.  The  whole  disturbance, 
however,  is  simply  a  tornado — it  may  be  a  very  small  one,  with 
the  phenomenon  of  the  waterspout  developed  in  the  same 
way  as  in  a  tornado  on  land. 

It  was  formerly  supposed  that  the  spout  consisted  of  water 
drawn  up  into  the  clouds  from  the  sea,  and  that  the  real  water- 
spout was  found  on  seas  and  lakes  only,  and  hence  the  name. 
It  is  true  that  a  considerable  amount  of  water  may  be  drawn 
up  from  the  sea,  but  this  is  merely  an  incidental  and  secondary 
matter  and  has  nothing  to  do  with  the  formation  of  the  spout. 
The  amount  of  water  drawn  up  is  so  small  generally  in  com- 
parison with  the  amount  of  rainfall,  that  the  latter  is  never 
observed  to  be  sensibly  affected  by  it  at  sea,  but  always  appears 
to  consist  of  fresh  water. 

When  we  consider  how  houses,  men,  and  various  kinds  of 


414  TORNADOES. 

heavy  bodies  and  debris  are  drawn  up  into  the  vortex  of  land 
tornadoes  and  thrown  out  above  in  all  directions,  as  explained 
in  §  258,  it  is  not  surprising,  but  to  be  expected,  that  much 
water  and  other  things  would  be  carried  up  in  tornadoes  at 
sea.  Here  the  very  centre  of  the  vortex  may  become  nearly 
a  vacuum,  and  hence  the  tendency  of  the  water  from  the  sur- 
rounding great  pressure  would  be  to  rise  up  nearly  32  feet ;  and 
having  risen  so  far,  or  at  least  to  a  considerable  height,  the 
rapidly  ascending  currents  would  carry  it  farther,  and,  being 
lashed  and  separated  into  drops,  it  would  then  be  carried  to 
still  great  heights,  as  raindrops  are  in  the  interior  of  a  tornado. 
We  have  accounts  of  not  only  water,  but  of  fish  and  frogs 
being  drawn  up  in  the  vortex  of  small  tornadoes  from  ponds 
•and  creeks,  leaving,  for  the  moment,  the  bottoms  of  the  latter 
dry,  and  afterwards  scattering  the  fish  and  frogs  over  the  neigh- 
boring land.  Tomlinson  says  :30 

"  Showers  of  fish  and  frogs  are  by  no  means  uncommon,  especially  in 
India.  One  of  these  showers,  which  fell  about  20  miles  south  of  Cal- 
'cutta,  is  thus  noticed  by  an  observer :  '  About  two  o'clock  P.M.  of  the 
42oth  inst.  (Sept.  1839)  we  had  a  very  smart  shower  of  rain,  and  with  it  de- 
scended a  quantity  of  live  fish,  about  three  inches  in  length,  and  all  of  one 
kind  only.  They  fell  in  a  straight  line  on  the  road  from  my  house  to  the 
tank,  which  is  about  40  or  50  yards  distant.  Those  which  fell  on  the 
hard  ground  were,  as  a  matter  of  course,  killed  from  the  fall ;  but  those 
which  fell  where  there  was  grass  sustained  no  injury,  and  I  picked  up  a 
large  quantity  of  them,  'alive  and  kicking,'  and  let  them  go  into  my 
tank.  The  most  strange  thing  which  ever  struck  me  in  connection  with 
this  event,  was,  that  the  fish  did  not  fall  helter-skelter,  everywhere,  or  here 
and  there,  but  they  fell  in  a  straight  line,  not  more  than  a  cubit  in 
breadth." 

The  following  is  taken  from  an  account  of  a  waterspout 
given  by  Sidney  B.  J.  Skirtchly,  H.  M.  Geo.  Survey:75 

"  Duringthe  summer  of  1870,  while  in  Deeping  Fen,  on  a  day  when  the 
wind  was  blowing  in  gusts,  carrying  the  dry  powdery  peat-dust  in  clouds 
before  it,  I  observed  a  whirling  column  of  dust  advancing  toward  me. 
It  was  like  those  small  pillars  so  frequently  seen  in  streets  of  a  town  on 
such  a  day,  but  it  was  considerably  larger,  being  from  15  to  20  feet  in 
height.  When  it  was  first  seen  it  was  advancing  from  the  far  side  of  a 
ground,  as  the  uninclosed  fields  are  called,  toward  me  at  the  rate  of 


WA  TERSPO  UTS.  41 5 

:about  six  miles  an  hour,  and  was  distant  some  500  yards.  It  moved  with 
an  unsteady,  staggering  motion,  accompanied  with  a  rushing  noise.  I 
stayed  to  watch  it  across  a  dike  about  15  feet  wide,  which  ran  directly 
across  its  path.  The  smaller  dikes  it  seemed  to  cross  without  affecting 
them  ;  but  on  reaching  the  one  in  question,  it  whisked  the  water  up  into 
a  waterspout  some  ten  feet  high  with  a  gurgling,  hissing  sound,  and 
steering  directly  across  the  dike  burst,  on  reaching  the  opposite  shore, 
projecting  a  considerable  quantity  of  water  upon  the  land.  This  effort 
seemed  to  spend  its  force,  for  the  dust-column  resumed  on  the  opposite 
land  was  but  small  in  proportion,  and  after  swaying  about  for  a  few 
yards,  -died  away." 

This  was  simply  a  whirlwind,  as  small  tornadoes  are  gen- 
erally called,  in  which  the  air  was  too  dry  and  the  energy  too 
small  to  develop  the  real  waterspout  of  particles  of  condensed 
vapor,  yet  it  seems  to  have  had  considerable  power  in  raising 
up  water  from  the  dike. 

In  addition  to  the  water  carried  up  in  the  spout  of  a  tornado 
there  is  often  also  much  spray  about  the  base  of  the  spout  which 
sometimes  assumes  the  form  somewhat  of  the  sand  and  dust 
cone  in  a  land  tornado,  causing  an  apparent  widening  of  the 
spout  at  the  base. 

269.  Small  waterspouts  observed  on  seas  and  lakes  in  clear, 
calm,  and  hot  weather  usually  arise  from  a  state  of  unstable 
equilibrium  in  the  lower  strata  of  the  atmosphere.  In  such 
cases  the  whirling  of  the  air  and  the  agitation  of  the  water  is 
first  observed  below,  and  afterwards  the  formation  of  a  cloud 
above,  and  finally  the  complete  spout,  unless  the  atmosphere 
is  very  dry.  When,  however,  the  air  is  very  moist, — near  the 
point  of  saturation, — such  spouts  extend  up  to  only  a  small 
height,  and  are  not  accompanied  by  any  rainfall,  since  they  are 
usually  too  small  and  continue  too  short  a  time  to  send  up  the 
vapor  to  so  great  a  height  that  it  can  be  condensed  and  col- 
lected into  drops  and  fall  as  rain. 

A  number  of  such  small  spouts  are  often  seen  at  one  time 
in  the  same  vicinity.  When  the  air  is  brought  to  the  unstable 
state  it  is  liable  to  burst  up  through  the  strata  above  at  several 
places  at  nearly  the  same  time,  and  then,  if  there  is  any  whirl- 
ing motion,  even  only  very  small  and  imperceptible,  as  in  the 


41 6  TORNADOES. 

case  of  the  water  in  a  basin,  there  is  a  concentration  of  this  mo- 
tion into  rapid  gyratory  motions  at  the  centre  of  each  one  of 
these  upbursts,  which  may  continue  to  increase  until  a  water- 
spout is  formed. 

M.  Defranc"  has  given  an  account  of  a  great  many  water- 
spouts of  the  class  which  occurs  mostly  in  weather  which  is- 
nearly  clear  and  calm.  He  says  : 

"  On  the  23d  of  June,  1764,  a  waterspout  was  seen  on  the  Seine,  which 
had  its  base  on  the  river  and  reached  up  into  the  clouds.  It  was  judged 
to  be  about  three  feet  in  diameter  where  it  touched  the  river.  There 
were  some  parts  transparent,  which  allowed  the  ascension  of  the  water 
to  be  seen.  It  finally  broke  at  about  one  third  of  its  height.  The  lower 
part  fell  in  rain,  the  upper  part  was  drawn  up  into  the  cloud  in  a  second 
of  time  and  the  phenomenon  was  followed  by  hail." 

This  seems  to  have  been  a  tall  spout  notwithstanding  the 
smallness  of  the  diameter.  The  air  in  the  vicinity  must  have 
been  nearly  calm,  and  in  the  unstable  state  up  to  a  consider- 
able altitude.  Being  a  very  tall,  slender  column  with  its  base 
upon  the  river,  the  friction  was  small,  and  so  it  approximated 
to  the  theoretical  case  of  no  friction  in  which  the  least  amount 
of  initial  gyratory  motion  would  bring  down  to  the  earth  a  fine 
thread-like  column  of  very  much  rarefied  and  cooled  air,  which 
gives  rise  to  a  slender  waterspout.  At  the  time  when  the  air  in 
the  central  column  is  not  quite  rarefied  and  cooled  sufficiently 
to  condense  the  vapor,  the  least  increase  in  gyratory  velocity 
brings  it  into  this  condition,  and  then  the  spout  darts  down 
from  the  cloud  above  almost  at  once.  Just  the  reverse  of  this 
takes  place  in  the  case  of  a  slender  spout  when  the  gyrations 
are  a  little  decreased  from  any  cause,  and  this  spout  seems  to 
have  been  thus  drawn  up.  The  lower  part  which  is  said  to 
have  fallen  as  rain  was,  no  doubt,  simply  the  water  raised  from 
the  river,  as  fish  and  frogs  are  said  to  be,  and  not  rain.  The 
falling  of  hail  indicates  that  the  ascending  currents  extended 
very  high  up  into  the  upper  and  very  cold  strata  of  the  atmos- 
phere 

Defranc  also  states : 

"On  May  17,  1763,  Captain  Cook  saw  six  waterspouts  on  Queen  Char- 
lotte Sound.  In  one  of  them  a  bird  was  seen,  and  in  arising  was  drawn  in 


WA  TERSPO  UTS.  41  / 

by  force  and  turned  around  like  a  spit.  Their  first  appearance  was  in- 
dicated by  a  violent  agitation  and  elevation  of  the  water.  When  the  tube 
was  first  formed  or  became  visible,  its  apparent  diameter  increased.  It 
then  diminished  and  became  invisible  at  its  lower  extremity." 

The  violent  agitation  and  heaping  up  of  the  water  before 
the  spouts  appeared  show  that  the  gyrations  and  barometric 
depressions  in  the  centre  existed  before  the  spouts  became  visi- 
ble, and  that  the  spouts  appeared  only  after  the  diminution  of 
tension  and  of  temperature  became  sufficient  to  condense  the 
vapor.  The  fact  of  the  bird's  being  drawn  in  and  whirled  around 
shows  that  the  air  is  really  drawn  in  from  ail  sides  and  up  in  a 
spiral  in  accordance  with  theory. 

The  frontispiece  to  the  title-page  is  the  view  of  a  water- 
spout as  observed  off  the  coast  of  Sicily,  and  sketched  by  Mr* 
Morey  in  August,  1876.  The  following  is  his  account  of  it : 

"  It  formed  during  a  comparatively  calm  and  clear  afternoon,  with 
the  temperature  of  the  atmosphere  not  much,  if  any,  higher  than  usual 
for  that  latitude  and  place.  The  wind  was  so  light  as  to  barely  cause  a 
slight  ripple  on  the  surface  of  the  sea,  but  sufficient  to  give  the  spout  a 
perceptible  motion  from  east  to  west.  Three  little  protuberances  first 
appeared  under  the  cloud,  the  centre  one  rapidly  elongating  connected 
with  the  water.  The  two  on  the  sides  increased  and  decreased  in  length, 
bat  never  reached  further  down  than  one  fifth  the  length  of  the  main 
spout. 

"It  lasted  about  twenty  minutes,  and  disappeared  shortly  after  the 
breaking  of  the  main  column  at  a  point  which  seemed  the  connection  be- 
tween the  funnel  and  the  water. 

"No  noise  accompanied  the  break  in  addition  to  the  noise  resem- 
bling a  cataract,  which  lasted  from  the  time  the  spout  connected  with  the 
water  to  the  break  up.  No  electrical  phenomena  were  noticed  at  all. 

"  A  rough  estimate  of  the  main  column  gave  its  height  between  700 
and  800  feet. 

The  stability  of  the  formation  during  the  twenty  minutes  of  its  dura- 
tion was  wonderful  in  the  extreme." 

Of  the  two  partial  spouts  or  funnel-shaped  protuberances 
on  each  side  the  one,  according  to  the  sketch,  seems  to  have 
caused  a  considerable  agitation  of  the  water  beneath  it. 

270.  Waterspouts  of  the  class  here  considered  are  very  often 
seen  along  the  eastern  coast  of  the  United  States  in  the  vicin* 


41 8  TORNADOES. 

ity  of  the  Gulf  Stream,  not  only  during  the  summer  season,  but 
likewise  in  the  winter.  On  the  Little  Bahama  Bank  as  many  as 
fifteen  have  been  seen  at  the  same  time.  The  following  ac- 
C0unt  of  them  is  given  by  an  officer  of  H.  M.  Surveying  Vessel 
"  Sparrow-Hawk,"  employed  in  the  West  Indies  :78 

"  I  have  noticed  that  the  first  movement  which  eventually  produces  a 
waterspout  is  a  whirlwind  on  the  surface  of  the  water,  gradually  increas- 
ing in  velocity  of  rotation  and  decreasing  in  diameter  as  it  travels  along 
before  the  prevailing  wind.  The  spray  is  lifted  up  to  a  height  of  from 
five  to  ten  feet,  and  then  gradually  melts  away,  assuming  the  appearance 
of  hot  air,  which  is  visible  (still  rotating)  to  a  similar  height  above  the 
spray.  A  motion  amongst  the  clouds  soon  becomes  apparent,  a  tongue 
is  protruded,  and  the  spout  becomes  visible  from  the  top  downwards. 

"On  one  occasion  a  portion  of  a  spout  appeared  for  a  moment  in  mid- 
air above  the  disturbances  on  the  surface  of  the  water. 

"  Although  these  appearances  are  commonly  called  waterspouts,  I  have 
been  informed  by  men  who  have  been  caught  in  them  that  they  contain 
no  water  and  should  be  properly  called  '  windspouts.'  The  small  fore- 
and-aft-rigged  schooners  that  ply  on  the  bank  do  not  fear  them,  although 
a  prudent  captain  would  probably  shorten  sail  to  one.  I  have  been  un- 
able taJiear  of  an  accident  having  occurred  through  a  vessel  being  caught 
in  a  waterspout. 

They  frequently  cross  the  land,  but  no  water  falls ;  they  take  up  any 
light  articles,  such  as  clothes  spread  out  to  dry,  straw,  etc.,  that  happen 
in  their  course,  but  have  never  been  known  to  carry  anything  with  them 
to  a  distance." 

It  is  seen  from  the  preceding  account  of  this  class  of  spouts 
that  the  whirlwind,  and  the  consequent  agitation  of  the  water 
beneath,  first  commence  and  gradually  increase  until  the 
strength  of  the  gyratory  motion  becomes  sufficient  to  bring 
down  the  spout,  and  that  this  first  appears  above  as  a  funnel 
or  short  spout,  and  then  becomes  visible  from  the  top  down- 
ward, the  same  as  in  the  larger  and  more  violent  land  torna- 
does. It  seems  that  there  is  no  water  carried  up  in  these 
small  whirlwinds  except  some  spray  to  a  short  distance  ;  but 
in  the  larger  ones,  and  especially  the  land  tornadoes,  some 
water  is  evidently  carried  up  when  they  pass  over  water.  If 
it  were  necessary  to  change  the  name,  which,  as  in  many  other 
things,  was  given  before  the  thing  was  understood,  it  would  be 


WA  TERSPO  UTS.  4 1 9 

•more  appropriate  to  call  them  vapor-spouts,  since  they  are  evi- 
dently composed  of  condensed  vapor,  and  no  amount  of  rotary 
motion  in  dry  air  would  produce  such  a  phenomenon. 

Where  the  atmosphere  is  clear  and  calm  over  a  river  or 
small  lake,  as  may  frequently  happen  where  it  is  surrounded 
by  highlands  and  forests,  and  the  air  is  very  nearly  saturated 
with  vapor,  very  diminutive  spouts  of  small  altitude  are  some- 
times seen.  Under  such  conditions  the  air  near  the  surface 
of  the  water  becomes  heated,  both  by  the  direct  and  reflected 
rays  of  the  sun,  and  a  stratum  of  air  of  small  depth  next  to  the 
surface  is  brought  to  the  unstable  state,  in  which  little  whirl- 
winds and  ascending  currents  originate  in  the  usual  way.  The 
air,  being  nearly  saturated,  would  have  to  ascend  to  only  a 
small  altitude  without  any  whirl  before  cloud  formation  would 
take  place,  and  this  being  so  near  the  earth's  surface,  a  slight 
whirling  of  the  air  is  able  to  bring  the  cloud  down  to  the  surface 
of  the  water  in  the  form  of  a  little  spout. 

271.  Such  small  spouts  have  been  observed,  under  very 
peculiar  circumstances,  to  be  hollow.  M.  Boue,79  in  the  year 
1850,  observed  three  small  waterspouts  at  the  same  time  on 
Lake  Janina,  from  the  top  of  a  high  mountain.  The  weather 
was  entirely  clear,  without  clouds  or  wind,  but  very  oppressive 
and  hot.  The  spouts  seemed  to  rise  up  from  the  lake,  and  he 
could  look  down  into  the  top  of  them  and  see  that  they  were 
hollow  in  the  middle.  The  same  seems  to  exist  in  some 
measure  in  large  spouts  both  on  sea  and  land,  as  is  indicated 
by  the  central  part  of  the  column  appearing  lighter  than  the 
surrounding  parts. 

This  hollowness,  or  less  density  of  the  condensed  vapor,  in 
the  middle,  arises,  no  doubt,  from  the  effect  of  the  centrifugal 
force  of  the  very  rapid  gyratory  velocity  near  the  centre,  in 
driving  the  condensed  vapor,  as  soon  as  formed,  out  from  the 
centre,  and  also  from  the  fact  that  the  central  part  is  so  rarefied 
and  cooled  down  that  but  little  vapor,  even  before  condensa- 
tion, can  approach  near  it,  since  it  is  mostly  condensed  before 
arriving  there  ;  just  as  in  the  vertical  ascent  up  into  the  region 
of  freezing  cold  very  little  uncondensed  vapor  is  left  after 


420  TORNADOES. 

having  ascended  to  that  altitude.  The  central  part  of  a  water- 
spout corresponds  in  temperature,  density,  and  capacity  for 
vapor  with  these  high  dry  strata  of  the  atmosphere  in  the 
surrounding  vicinity,  as  is  understood  from  Fig.  I,  §  233. 

In  fact  there  seems  to  be  a  slightly  analogous  phenomenon 
even  in  cyclones,  in  which  the  clouds  are  frequently  less  dense, 
and  even  entirely  disappear  sometimes,  in  the  central  part, 
giving  rise  to  what  is  called  "  the  eye  of  the  storm,"  though  the 
explanation  is  only  in  part  the  same. 

HAIL-STORMS. 

272.  A  hail-storm  is  simply  a  tornado  in  which  the  ascend- 
ing currents  are  so  strong,  and  reach  so  high  up  into  the  upper 
strata  of  the  atmosphere,  that  the  rain-drops  are  carried  up 
into  the  cold  regions  above,  and  into  the  central  part  within  the 
isobaric  and  isothermic  surface  of  the  freezing-point,  where 
they  are  frozen  into  hail.  In  fact  hail,  as  well  as  rain,  is 
almost  a  universal  accompaniment  of  a  tornado,  and  so,  as  the 
latter,  it  is  usually  found  in  the  S.E.  quadrant  of  a  cyclone 
and  at  a  considerable  distance  from  the  centre,  as  has  been 
shown  to  be  the  case  in  Russia  by  Klosovsky  from  observation 
(§  3.11).  Finley  says,72  in  his  account  of  the  tornadoes  of  May 
29  and  30,  1879: 

"  In  referring  to  the  several  storm  descriptions,  it  will  be  found  that 
rain  and  hail  invariably  preceded  the  tornado  cloud  from  ten  to  thirty 
minutes,  nearly  always  attended  by  a  southerly  wind." 

But  this  applies  mostly  to  the  more  violent  tornadoes,  such 
as  were  investigated  by  him,  and  not  to  every  class  of  atmos- 
pheric phenomena  which  we  have  included  under  the  generic 
name  tornado. 

It  has  been  shown  in  §  233  that  every  isobaric  and  isother- 
mic surface,  however  high  above  the  earth's  surface,  would  in 
a  perfectly  regular  tornado,  and  in  the  case  of  no  friction,  be 
brought  down  by  the  centrifugal  force  of  the  gyratory  motion 
to  the  earth's  surface  near  the  centre  of  the  tornado,  as 
represented  in  Fig.  i.  The  horizontal  and  isothermic  surface. 


HAIL-STORMS. 


421 


therefore,  high  up  in  the  air,  which  separates  the  strata  of 
freezing  temperature  above  from  those  of  a  non-freezing  tem- 
perature below,  would,  in  case  of  no  friction,  be  brought  down 
by  tornadic  action  to  the  earth's  surface  at  c.  The  effect  of 
friction,  however,  prevents  its  bringing  the  freezing  atmosphere 
entirely  down,  or  rather  its  so  expanding  and  rarefying  the  air 


Fig.  II. 

in  the  central  part  that  the  air  in  consequence  is  reduced  to 
the  freezing  temperature  down  to  the  earth's  surface.  But 
still  the  air  of  freezing  temperature  is  brought  down  in  the  central 
part  in  the  form  of  a  funnel,  considerably  below  the  general 
level  of  its  base  when  undisturbed,  just  as  it  has  been  shown 
the  cloud  region  is,  Fig.  7,  and  as  is  represented  by  a'c'b',  Fig. 
1 1,  in  which  the  unshaded  part  represents  the  unclouded  air 
below  and  beyond  the  surface  of  incipient  condensation,  here 


422  TORNADOES. 

supposed  to  be  brought  entirely  down  to  the  earth's  surface 
A  B ;  the  darker  shaded  portion,  the  part  in  which  the  vapor  is 
condensed  to  ordinary  cloud ;  and  the  lighter  shading  above, 
the  part  where  the  vapor  is  converted  directly  to  snow,  and  the 
rain-drops,  carried  up  by  the  ascending  currents,  to  hail.  The 
height  of  the  surface  of  incipient  freezing,  or  temperature  of 
0°  C,  where  the  temperature  of  the  air  at  the  earth's  surface  is 
given,  may  be  ascertained  in  the  same  way  as  the  temperature 
at  any  given  height,  as  explained  in  §  27. 

273.  In  a  torrado  the  air  at  and  near  the  earth's  surface 
is  drawn  in  and  ascends  on  all  sides  until  it  arrives  at  the 
surface  of  incipient  condensation,  represented  by  the  lower 
line  ab,  brought  down  to  the  earth  on  each  side  of  the  centre 
at  /,  at  which  surface,  as  has  already  been  explained,  cloud- 
formation  commences.  In  its  further  ascent  and  approach 
toward  the  interior  central  part  the  vapor  contained  in  it  is 
gradually  condensed,  and  the  temperature  of  the  air  reduced, 
until  it  arrives  at  the  surface  of  incipient  freezing,  either  up  at 
the  undisturbed  level  beyond  the  influence  of  tornadic  action 
as  at  a'  or  b',  or  where  that  surface  is  brought  down  below  this 
level  near  the  centre  in  the  region  of  c' .  As  the  air,  with  the 
uncondensed  vapor  yet  remaining,  enters  above  and  within 
this  surface,  the  vapor  left  is  gradually  frozen  to  snow,  and 
the  higher  it  ascends  the  more  of  it  is  so  changed.  This  snow, 
however,  never  falls  to  the  earth  in  the  summer  season,  but 
melts  soon  after  falling  below  the  level  of  incipient  freezing. 
In  the  winter  season,  at  times  when  this  level  is  not  very  far 
above  the  earth's  surface,  it  reaches  the  surface  as  soft  snow, 
where  there  is  no  tornadic  action  and  only  gentle  ascending 
currents. 

In  the  ascending  current  of  a  tornado,  as  in  that  of  the 
equatorial  calm-belt  or  of  a  cyclone,  the  rain-drops  are  formed 
down  in  the  cloud  region  and  carried  upward  until  they  be- 
come too  large  to  be  supported  by  the  current,  and  so  fall  to 
the  earth,  as  explained  in  §  in.  In  a  tornado,  however,  the 
ascending  current  is  often  so  strong  that  the  rain  is  supported 
until,  by  the  blending  of  the  small  drops  by  coming  in  contact, 


HAIL-STORMS.  423 

very  large  drops  are  formed,  and  the  strong  ascending  currents 
often  extend  so  high  that  these  large  drops  are  carried  away 
up  into  the  region  of  freezing  temperature,  represented  by  the 
upper  lighter  shading  in  the  preceding  figure.  They  are  there 
frozen,  and  after  having  been  carried  up  and  outward  above  to 
a  distance  from  the  centre  where  the  ascending  current  is  not 
strong  enough,  by  the  formula  of  §  247,  to  keep  them  up,  they 
slowly  descend,  and,  receiving  additions  of  ice  as  they  fall,  as 
long  as  their  temperature  remains  below  zero,  from  the  rain 
below,  which  is  being  either  kept  suspended  in  the  air  or  being 
carried  farther  up,  they  finally  fall  to  the  earth  as  solid  hail- 
stones. 

274.  But  the  origin  of  the  hailstone  is  often  not  a  rain- 
drop, but  a  bunch  of  snow  formed  in  the  snow  region,  and 
moistened  by  the  rain  carried  up  into  this  region  before  it  has 
had  time  to  become  frozen  into  hail.  This  moist  snow  is  kept 
up  there  until  it  freezes,  and  after  that,  while  being  kept  up 
there,  and  after  it  commences  to  fall,  as  long  as  its  temperature 
remains  below  zero  it  continues  to  receive  a  coating  of  ice 
from  the  rain  which  is  carried  up  past  it  and  that  through 
which  it  falls.  As  it  grows  and  is  carried  outward  above 
where  the  ascending  current  is  weaker,  it  finally  becomes  too 
heavy  to  be  kept  suspended  in  the  air,  and  it  falls  to  the  earth 
a  hailstone,  with  a  kernel  of  frozen  snow  in  its  centre. 

In  such  a  case  we  may  imagine  the  soft  ball  of  snow  to 
have  originated  in  the  snow  region  at  m  and  then  to  have  been 
kept  partially  suspended  and  to  have  been  carried  up  and  out 
slowly  from  the  centre  to  a  distance  where  it  could  drop  down, 
having  become  meanwhile  reduced  to  a  low  temperature,  and 
that  on  its  way  down  it  received  a  coating  of  ice  from  the 
small  ascending  rain-drops,  or  others  with  which  it  came  in 
contact  during  its  fall,  and  that  it  finally  reached  the  earth  at  n. 

It  often  happens,  however,  that  in  falling  very  gently 
where  the  ascending  current  at  no  great  distance  from  the  vor- 
tex is  not  quite  but  nearly  sufficient  to  keep  it  suspended,  it 
is  drawn  in  again  by  the  indrawing  currents  from  all  sides  to- 
ward the  vortex,  as  the  scud  clouds  under  the  rim  of  the  tor- 


424  TORNADOES. 

nado  cloud,  §  266,  where  the  ascending  current  is  sufficient  to 
carry  it  up  again  into  the  snow  region,  where  it  receives  a 
coating  of  snow  moistened  by  the  small  rain-drops  carried  up 
into  the  snow-region  before  they  freeze.  This  coating  now 
becomes  frozen  solid,  and  the  whole  mass,  it  may  be,  is  re- 
duced considerably  below  zero  temperature  before  it  is  carried 
out  above,  where  it  can  gradually  drop  down  again  toward  the 
earth ;  and  in  falling,  even  through  the  lower  part  of  the  snow- 
region  where  there  is  little  snow,  but  mostly  rain-drops  not  yet 
frozen,  it  receives  another  coating  of  solid  ice ;  for  its  temper- 
ature having  been  reduced  considerably  below  zero,  it  contin- 
ues to  freeze  the  rain  coming  in  contact  with  it  for  a  long  dis- 
tance after  having  passed  down  into  the  cloud  region.  But  in 
gently  falling  down  it  may  be  drawn  in  a  second  time  toward 
the  centre  and  be  carried  up  by  the  ascending  current  into  the 
snow-region  and  receive  another  coating  of  wet  snow  over  the 
last  one  of  solid  ice,  and  in  falling  receive  another  coating  of 
solid  ice  in  the  same  manner  as  before.  This  process  may  be 
repeated  a  number  of  times,  in  each  of  which  the  hailstone, 
disregarding  its  gyratory  motion  all  the  while,  describes  a  kind 
of  orbit,  not  returning  into  itself,  somewhat  as  represented  in 
Fig.  11,  until  finally  it  is  carried  out  above  so  far  from  the 
centre,  or  the  strength  of  the  tornado  becomes  so  much  weak- 
ened, that  it  is  no  longer  carried  in  toward,  and  up  in,  the  cen- 
tral part,  but  falls  to  the  earth  a  hailstone  with  a  snow-kernel 
and  a  number  of  alternating  concentric  coatings  of  solid  ice  and 
frozen  wet  snow. 

In  this  case  we  may  suppose  the  small  snowball  to  have 
originated  at  p  and  to  have  been  carried  up  and  out,  and  then 
to  have  fallen  down  and  to  have  been  drawn  in  toward  the 
centre  several  times,  until  finally  it  was  carried  out  so  far,  and 
had  grown  to  be  so  heavy,  that  it  was  not  brought  in  toward 
the  centre  but  dropped  down  to  the  earth  at  q,  Fig.  n. 

Hail-storms  occur  mostly  in  the  summer  season.  In  the 
winter  season  the  plane  of  incipient  freezing  is  so  low  that 
there  is  little  or  no  rain-cloud  region  in  which  large  rain-drops 
can  be  formed  and  in  which,  after  having  been  frozen  above, 


HA  I L- STORMS.  42  5 

they  are  increased  in  size  in  falling  through.  Winter  hail,  there- 
fore, consists  of  only  very  small  particles  of  frozen  water. 

275.  A  remarkable  example  of  hailstones  with  concentric 
coatings  was  observed  at  Northampton,  Mass.,  June  20,1870, 
an  account  of  which  has  been  given  by  Mr.  Houry.85  In  this 
case  hailstones  fell  weighing  over  a  half  pound,  and  most  of 
them  were  formed  of  concentric  layers,  like  the  coats  of  an 
onion.  Mr.  Houry  states  that  in  one  of  them  he  counted 
thirteen  layers,  indicating,  as  he  says,  that  it  had  passed 
through  as  many  strata  of  snowy  and  vaporous  clouds.  The 
true  explanation  is,  that  it  oscillated  as  many  times  between 
the  rain-cloud  and  the  snow-cloud  regions,  or,  in  other  words, 
that  it  performed  six  or  seven  revolutions  with  the  lower  part 
of  its  orbit  in  the  rain-cloud,  and  the  upper  part  in  the  snow- 
cloud,  in  the  manner  represented  in  Fig.  II. 

In  corroboration  of  the  preceding  theory  of  the  formation 
of  hail,  and  as  an  exemplification  of  the  motions  of  a  hailstone, 
as  represented  above,  the  following  extract  from  a  letter  of 
Mr.  John  Wise,  the  balloonist,  written  to  the  New  York  Trib- 
une in  Feb.,  1857,  w^tn  reference  to  an  ascent  which  he  made 
in  a  tornado,  is  given  here,  from  which  it  is  seen  that  he  de- 
scribed similar  orbits  with  his  balloon  in  the  tornado  cloud  :88 

"This  storm  originated  nearly  over  the  town  of  Carlisle,  Pennsyl- 
vania, on  the  1 7th  of  June,  1843.  I  entered  it  just  as  it  was  forming. 
The  nucleous  cloud  was  just  spreading  out  as  I  entered  the  vortex  un- 
suspectingly. I  was  hurled  into  it  so  quickly  that  I  had  no  opportunity 
of  viewing  the  surroundings  outside,  and  must  therefore  confine  this 
relation  to  its  internal  action.  On  entering  it  the  motions  of  the  air 
swung  the  balloon  to  and  fro,  as  around  in  a  circle,  and  a  dismal,  howl- 
ing noise  accompanied  the  unpleasant  and  sickening  motion,  and  in  a 
few  minutes  thereafter  was  heard  the  falling  of  heavy  rain  below,  resem- 
bling in  sound  a  cataract.  The  color  of  the  cloud  internally  was  of  a 
milky  hue,  somewhat  like  a  dense  body  of  steam  in  the  open  air,  and  the 
-cold  was  so  sharp  that  my  beard  became  bushy  with  hoar-frost.  As 
there  were  no  electrical  explosions  in  this  storm  during  my  incarcera- 
tion, it  might  have  been  borne  comfortably  enough  but  for  the  seasick- 
ness occasioned  by  the  agitated  air-storm.  Still,  I  could  hear  and  see, 
and  even  smell,  eveiything  close  by  and  around.  Little  pellets  of  snow 
{with  an  icy  nucleus  when  broken)  were  pattering  profusely  around  me 


426  TORNADOES. 

in  promiscuous  and  confused  disorder,  and  slight  blasts  of  wind  seemed 
occasionally  to  penetrate  this  cloud  laterally,  notwithstanding  there  was 
an  upmoving  column  of  wind  all  the  while.  This  upmoving  stream 
would  carry  the  balloon  up  to  a  point  in  the  upper  cloud,  where  its  force 
was  expended  by  the  outspreading  of  its  vapor,  whence  the  balloon 
would  be  thrown  outward,  fall  down  some  distance,  then  be  drawn  into- 
the  vortex,  again  to  be  carried  upward  to  perform  the  same  revolution, 
until  I  had  gone  through  the  cold  furnace  seven  or  eight  times ;  and  all 
this  time  the  smell  of  sulphur,  or  what  is  now  termed  ozone,  was  percep- 
tible, and  I  was  sweating  profusely  from  some  cause  unknown  to  me, 
unless  it  was  from  undue  excitement.  The  last  time  of  descent  in  this 
cloud  brought  the  balloon  through  its  base,  where,  instead  of  pellets  of 
snow,  there  was  encountered  a  drenching  rain,  with  which  I  came  into- 
a  clear  field,  and  the  storm  passed  on." 

The  "cold  furnace"  through  which  he  passed  seven  or 
eight  times  was  most  probably  in  and  near  the  interior  and 
upper  part  of  the  vortex,  in  the  vicinity  of  c't  Fig.  11,  where 
the  snow-cloud  and  cold  upper  strata  are  brought  down  in  the 
form  of  the  funnel-cloud  in  tornadoes,  or,  it  may  be,  still  lower 
in  the  form  of  a  waterspout,  for  it  must  be  borne  in  mind  that 
the  balloon  could  be  carried  into  this  snow-region,  or  at  least 
into  a  region  of  very  low  temperature,  without  ascending  to 
very  high  altitudes  by  being  carried  close  into  the  centre  where 
this  region  is  brought  down.  Low  temperatures  are  reached 
by  going  in  toward  the  centre  as  well  as  by  ascending  to  higher 
altitudes. 

The  small  pellets  seem  to  have  originated  in  small  rain-drops- 
which,  being  carried  up  into  the  snow-cloud,  received  a  coating 
of  snow,  but  had  not  received  a  subsequent  one  of  ice  when  they 
struck  his  balloon. 

The  motions  of  the  balloon  in  which  M.  H.  Lecocq  recently 
ascended  from  Paris  seem  to  have  been  similar,  on  entering 
up  through  the  base  into  a  thunder-cloud,  to  those  of  Mr.. 
Wise's  balloon.  According  to  the  account  :91 

"  The  balloon,  influenced  by  electrical  attraction,  rose  toward  the 
cloud,  accompanied,  or  rather  preceded,  by  the  pieces  of  paper  which  the 
balloonists  had  thrown  from  their  basket.  At  20  minutes  of  8,  and  at 
a  height  of  iioo  meters,  the  balloon  entered  a  cloud-mass  of  greenish- 
gray  color,  which  immediately  shut  out  from  them  all  sight  of  the 


HAIL-STORMS. 

earth.  .  .  .  The  balloon  constantly  rotated  and  ascended  and  de- 
scended without  the  interference  of  the  balloonists ;  and,  what  is  a 
very  rare  thing  in  a  balloon,  they  felt  almost  constantly  a  very  consider- 
able wind,  which  shook  the  balloon  and  gave  to  the  basket  a  swinging 
motion  of  considerable  amplitude." 

The  account  further  states  : 

"  At  certain  times  a  sensation  as  of  a  current  of  cold  air  was  very 
perceptible.  This  was  followed  immediately  by  a  rapid  ascension,  and 
the  expelled  gas  descended  even  to  the  basket.  During  one  of  these 
ascents  the  balloon  reached  a  height  of  1600  meters,  which  was  the 
maximum." 

The  balloon  was  not  drawn  into  the  cloud  by  electrical 
attraction,  but  carried  up  into  it  by  the  ascending  currents, 
which  gave  rise  to  the  cloud,  and  with  a  velocity  less  than  in 
the  case  of  the  pieces  of  paper,  because  the  latter  had  more, 
surface  exposed  to  the  ascending  currents,  in  proportion  to 
their  mass,  than  the  balloon.  At  the  height  of  1100  meters, 
the  vapor  began  to  be  condensed  to  form  the  base  of  the  cloud. 
The  relative  air-current  in  this  case  arose  from  the  air's  ascend- 
ing and  being  drawn  in  obliquely  toward  the  centre  past  the 
balloon,  which  was  acted  upon  by  the  force  of  gravity  and  the 
centrifugal  force  of  the  gyrations.  The  balloon  ascended 
rapidly  when  drawn  in  near  the  centre  where  the  ascending 
current  is  rapid,  and  descended  when  carried  out  above  to 
where  the  ascending  currents  are  weak.  It  was  near  the  cold 
centre  where  the  sensation  of  a  cold  current  was  experienced, 
and  then  the  balloon  ascended  rapidly,  because  here  the 
ascending  current  is  strong. 

In    this    thunder-cloud  there  was  no    doubt  considerable 
tornadic  action,  as  indicated  by  the  observed  constant  rotation 
and  ascent  and  descent  of  the  balloon,  though  not   enough  to 
.give  rise  to  either  hail  or  a  waterspout. 

276.  The  shape  of  hailstones  varies  very  much.  Some  are 
like  a  disk  or  very  oblate  spheroid.  If  for  any  reason  the  hail- 
stone becomes  the  least  flattened,  the  ascending  current  which 
keeps  it  suspended  for  a  time  in  the  air  also  keeps  its  shortest 
diameter  perpendicular  to  the  current,  and  hence  it  then. 


.428  TORNADOES. 

increases  most  on  the  edges.  Others  are  of  a  pyramidal  form, 
or  of  an  irregular  oval  shape  with  uneven  surface.  They  also 
appear  sometimes  to  be  fragments  of  large  pieces  of  ice,  broken 
by  collision  with  one  another  by  the  gyratory  vortex  of  the 
tornado. 

In  Iowa,  in  1880,  according  to  Dr.  Hinrichs, 

"  Hailstones  12  inches  in  circumference  have  been  measured  in  Sac 
County.  In  Davis  County  a  flattened  disk  of  hail  measured  4^  inches 
in  diameter,  and  was  2  inches  thick.  In  Iowa  County  a  group  of  ice 
crystals  fell,  2  inches  in  length,  if  inches  wide,  and  I  inch  thick." 

From  the  report  on  the  tornadoes  of  May  29  and  30,  iS/Q,72 
have  been  extracted  the  following  notices  of  some  very  extraor- 
dinary hail-falls  : 

In  the  Lee's  Summit  tornado,  Mrs.  Irwin  stated  that  "  hail 
like  '  large  chunks  of  ice,'  with  very  little  rain,  fell  just  after  the 
storm-cloud  passed." 

In  the  Delphos  tornado,  it  is  stated  : 

"On  the  farm  of  Mr.  Peter  Bock,  in  the  adjoining  township  of 
Fountain,  about  4  miles  W.  of  the  storm's  centre,  and  during  the  hail- 
storm that  preceded  the  tornado,  masses  of  ice  fell  as  large  as  a  man's 
head,  breaking  in  pieces  as  they  struck  the  earth.  One  measured  13 
inches  in  circumference,  another  15,  and  a  hole  made  by  one  that  fell 
near  the  place  of  Mr.  J.  H.  Kams  measured  7  inches  across  one  way 
•  and  8  the  other.  This  immense  fragment  of  aerial  ice  broke  into  small 
pieces,  so  that  its  exact  size  could  not  be  determined." 

It  is  also  stated  in  the  copy  of  a  letter  from  Mr.  Billingsley, 
of  Delphos,  that  several  hailstones  fell  which  measured  12  to 
15  inches  in  circumference  and  I  to  2  inches  in  diameter. 
These  must  have  been  in  the  form  of  disks  the  thickness  of 
which  was  from  I  to  2  inches. 

In  the  account  of  the  Lincoln  County  tornado,  it  is  stated : 

"  At  first  the  hailstones  were  about  the  size  of  marbles,  but  they 
rapidly  increased  in  diameter  until  they  were  as  large  as  hens'  eggs  and 
very  uniform  in  shape.  After  the  precipitation  had  continued  about 
fifteen  minutes,  the  wind  ceased  and  the  small  hail  nearly  stopped,  when 
there  commenced  to  fall  perpendicularly  large  bodies  of  frozen  snow  and 
ice,  some  round  and  smooth  and  as  large  as  a  pint  bowl,  others  inclined 


CLOUD-BURSTS.  429- 

to  be  flat,  with  scalloped  edges,  and  others  resembled  rough  sea-shells. 
One  of  the  latter,  after  being  exposed  an  hour  to  the  sun,  measured  14 
inches  in  circumference." 


CLOUD-BURSTS. 

277.  Considering  the  strong  ascending  currents  in  tor- 
nadoes, and  their  great  supporting  power,  as  deduced  from 
theory  and  exemplified  in  numerous  cases  of  observation,  it  is 
not  to  be  wondered  at  if  great  accumulations  of  rain  and  hail 
are  sustained  for  a  while  by  these  currents  at  a  considerable 
altitude  in  the  vortex  of  the  tornado,  and  then,  on  account  of 
a  sudden  weakening  or  breaking  up  of  the  tornado  for  some 
reason,  a  great  amount  of  rain  and  hail  should  sometimes  fall 
to  the  earth  in  a  short  time.  Such  abundant  and  sudden  pre- 
cipitations are  called  cloud-bursts.  If  the  velocity  of  the  ascend- 
ing current  in  the  interior  is  not  so  great  that  the  rain  is  all 
carried  up  where  the  current  is  outward  from  the  vortex,  or 
where  this  outward  current  and  the  centrifugal  force  of  the 
gyrations  together  are  able  to  drive  it  out  where  it  can  fall 
through  the  weaker  ascending  current,  and  yet  is  great 
enough  to  prevent  its  falling  back,  then  in  the  whole  of  the 
lower  part  of  the  cloud  in  the  central  part  of  the  tornado,  even 
up  to  an  altitude  of  three  miles  or  more,  there  may  be  a  great 
accumulation  of  rain,  prevented  by  the  ascending  current  from 
falling,  and  also  by  the  centripetal  in-drawing  current  below  a 
given  level  from  being  carried  out  and  dispersed.  Of  course,  a 
considerable  part  of  the  energy  of  the  tornado  is  required  to 
support  this  mass,  so  that,  as  this  increases,  the  strength  of  the 
ascending  current  is  weakened,  until  finally  the  whole  mass 
suddenly  falls.  Or  the  whole  system  may  become  weak  and 
break  up  from  some  other  cause,  when  the  same  result  follows. 
This  is  especially  liable  to  occur  in  mountainous  regions ;  for 
if  we  suppose  that  a  tornado  thus  heavily  charged  with  rain  is 
moving  toward  the  side  of  a  mountain,  its  coming  in  contact 
with  it  would  interfere  very  much  with  the  gyrations  and 
energy  of  the  tornado,  and  tend  to  break  up  the  whole  system 
almost  at  once,  and  let  the  whole  accumulation  of  water  drop 


-43°  TORNADOES. 

suddenly  down.     Hence  cloud-bursts  most  frequently  occur  on 
•mountain-sides. 

278.  The  water  in  cloud-bursts  does  not   generally  fall   as 
rain,  but  is  poured  down.     Long  before  the  ascending  current  is 
so  reduced  as  to  allow  it  to  fall  in  drops,  the  water  seems  to  col- 
lect together  at  certain  places  and  to  force  its  way  downward, 
through  the  ascending  current,  in  a  stream.     This  it   would 
naturally  do,  since  we    cannot  suppose  that  it  is  ever  evenly 
•distributed   over  any  given  place,  or  that   the  velocity  of  the 
ascending   current    is   exactly  the   same  at   all  points  in   the 
same  vicinity.     A  considerable  body  of  water  having  been  col- 
lected at  certain  points,  it  is  there  able  to  force  its  way  down, 
•and  it  draws  into  its  train  much  more  from  all  sides  on  its  way, 
so  that  continuous  streams  of  water  are  formed  and  kept  up 
for  several  minutes,  during  which  an  immense  amount  of  water 
falls  on  a  number  of  small  spots,  while  not  even  rain-drops  fall 
between  on  account  of  the  strength  of  the  ascending  current, 
through  which  water  can  only  be  poured  down.     Having  col- 
lected in  large  masses  and  once  made  an  opening  for  itself  at 
one  or  more  places,  the  velocity  of  the  streams  is  gradually 
accelerated,  since  the  ascending  current  then  is  not  able  to  sup- 
port them,  so  that  on  reaching  the  earth  the  velocity  may  be- 
come immensely  great,  and  the  streams  strike  with  great  force. 
Each  one  of  these  descending  streams  may  make  a  great  hole 
or  basin  in  the  ground ;    and  on  a  steep  mountain-side,  if  the 
stream  continues  for  a  short  time  only,  it  may  give   rise  to  a 
mountain  slide,  or  at  least  to   a  great   ravine,  and    carry  rocks 
and  trees  with  it  down  the  mountain-side. 

279.  Immediately  after  the  great  tornado  at  Hollidaysburg, 
Pa.,  on  the  iQth  of  June,  1838,  Espy34  visited  the  vicinity  and 
examined  the  sides  of  the  ridges  and  mountains.     He  found  a 
great  many  holes  eight  or  ten  meters  in  diameter  and  one  or 
two  in  depth,  according  to  the  nature  of  the  soil  and  depth  of 
the  rock,  and  the  sides  often  cut  almost  perpendicularly  down 
•on  the   upper  sides,  but  entirely  washed   out  below,  so  as  to 
form  the  commencement  of  a  ravine.     Sometimes  the  current 
descending  through  the  atmosphere  seemed  to  strike  the  earth 


CL  0  UD-B  URSTS.  431 

with  so  great  a  force  that  it  made  a  great  hole  or  basin  and 
then  rebounded  so  as  not  to  strike  the  earth  again  on  the 
mountain-side  for  a  considerable  distance  below.  Several  of 
these  holes  were  often  found  close  together  in  the  same  vicin- 
ity, indicating  that  the  water  was  poured  down  at  the  same  time 
through  several  openings  made  in  the  current  of  ascending  air 
by  the  concentration  of  large  bodies  of  water  at  these  places. 

With  regard  to  a  ridge  a  half-mile  west  of  Hollidaysburg, 
he  says : 

"  On  examining  the  northern  side  of  this  ridge,  large  masses  of  gravel 
and  rocks  and  trees  and  earth,  to  the  number  of  22,  were  found  lying 
at  the  base  on  the. plain  below,  having  been  washed  down  from  the 
side  of  the  ridge  by  running  water.  The  places  from  which  these 
masses  started  could  easily  be  seen  from  the  base,  being  only  about  30 
yards  up  the  side.  On  going  to  the  head  of  these  washes,  they  were  found 
to  be  nearly  round  basins  from  i  to  6  feet  deep,  without  any  drains  lead- 
ing into  them  from  above.  The  old  .leaves  of  last  year's  growth,  and 
-other  light  materials,  were  lying  undisturbed  above,  within  an  inch  of 
the  rim  of  these  basins,  which  were  generally  cut  down  nearly  perpen- 
dicularly on  the  upper  side,  and  washed  out  clean  on  the  lower.  The 
greater  part  of  these  basins  were  nearly  of  the  same  diameter,  about  20 
feet,  and  the  trees  that  stood  in  their  places  were  all  washed  out. 
Those  below  the  basin  were  generally  standing,  and  showed  by  the  leaves 
and  grass  drifted  on  their  upper  side  how  high  the  water  was  in  running 
down  the  side  of  the  ridge ;  on  some  it  was  as  high  as  3  feet.  It  proba- 
bly, however,  dashed  up  on  the  trees  above  its  general  level." 

In  an  account  of  a  remarkable  storm  which  occurred  at 
Catskill,  July  26,  1819,  it  is  stated  that  "  the  rain  at  times  de- 
scended in  very  large  drops,  and  at  times  in  streams  and 
sheets."  In  the  mountainous  regions  of  the  States  and  Terri- 
tories of  the  United  States  immediately  east  of  the  Rocky 
Mountain  range,  where  tornadoes  especially  abound,  the  im- 
mense amount  of  water  which  sometimes  drops  down  suddenly 
from  the  clouds  and  collects  in  the  ravines,  and  the  valleys  into 
which  they  lead,  often  cause  great  floods,  which  are  especially 
disastrous  on  account  of  their  suddenness,  which  leaves  little 
or  no  time  for  escape.  The  following  is  a  newspaper  account 
of  cloud-bursts  which  occurred  near  Fort  Keogh,  Mont.,  a  few 


432  TORNADOES. 

years  ago,  and  which  are  merely  samples  of  similar  occurrences, 
which  frequently  take  place  in  Montana  and  adjacent  territories. 

"  Word  has  been  received  from  Simmons'  sheep  corral,  on  the  Amer- 
ican fork  of  the  Mussel  shoal,  that  a  cloud-burst  there  Monday  evening 
destroyed  800  head  of  sheep.  The  cloud  exploded  at  the  head  of  Dry 
Run  Creek  and  came  pouring  down  in  a  solid  wall  32  feet  high,  car- 
rying off  nearly  the  entire  herd,  and  almost  drowning  a  herder.  The 
carcasses  of  the  animals  are  strewn  along  the  river  for  a  distance  of 
1 6  miles  below  the  scene  of  the  disaster.  The  upper  Yellowstone 
valley  was  visited  yesterday  by  a  terrific  hail-storm,  which  rooted  up  and 
destroyed  every  growing  thing  in  a  strip  of  country  six  miles  wide.  Near 
Merill  occurred  a  cloud  hail-burst.  For  half  an  hour  the  hail  was. 
beyond  description.  There  were  drifts  of  hail  14  inches  deep  in  some 
places.  There  was  little  rain  accompanying  the  hail — simply  one  sheet 
of  hail  came  pouring  down." 

The  Signal  Service  observer  at  Fort  Elliott,  Tex.,  reports:93 

"  A  thunder-storm  began  at  4.10  P.M.  and  ended  at  7.40  P.M.,  moving 
from  southwest  to  northeast.  Hail  began  at  5.18  P.M.  and  ended  at  5.26 
P.M.,  the  hailstones  being  spheroidical  in  shape  and  about  two  inches  in 
diameter;  formation,  solid  snow.  The  '  breaks '  (hills)  at  the  foot  of 
the  plains  several  miles  northwest  of  station  were  absolutely  white  with 
hailstones  for  three  hours  after  the  storm.  This  was  observed  by  every- 
body at  the  station  ;  on  the  morning  of  the  26th  I  walked  down  to  the 
Sweetwater  Creek,  three  fourths  of  a  mile  distant,  and  saw  great  banks 
of  hailstones  which  had  been  washed  down  during  the  night.  The  bot- 
toms along  the  Sweetwater  were  literally  covered  with  banks  of  hail- 
stones from  six  to  eight  feet  in  depth.  It  was  estimated  that  there  was 
enough  hail  to  cover  ten  acres  to  a  depth  of  six  feet.  The  hailstones 
killed  five  horses  which  were  out  on  the  prairie  on  a  ranch  six  miles 
north  of  station.  The  Sweetwater  Creek  was  higher  than  ever  known 
before,  the  freshet  destroying  nearly  the  entire  post  garden.  The  high 
water  is  supposed  to  have  been  caused  by  a  '  cloud-burst'  at  or  near  the 
foot  of  the  plains,  where  the  Sweetwater  has  its  source  ;  there  was  only 
0.36  inch  of  rainfall  at  the  station.  On  Sunday,  May  27th,  hailstones 
were  collected  on  the  banks  of  the  Sweetwater,  which  had  been  washed 
down  and  lay  in  drifts  6  feet  deep,  actual  measurement  by  the  observer." 

280.  From  these  accounts  and  many  other  similar  ones 
which  might  be  cited,  it  is  evident  that  the  water  in  such  cases 
does  not  fall  as  rain,  but  is  poured  down  in  streams ;  and  this 
is  especially  evident  from  the  observed  effects  of  the  Hollidays- 


CLOUD-BURSTS.  433 

burg  tornado,  by  which  great  holes  and  basins  were  made  in  the 
ground,  and  the  lightest  materials  on  the  margins  of  these  on 
the  upper  sides  were  not  washed  away;  and  the  reason  of  this 
evidently  is  that  the  accumulated  water  in  the  cloud  is  poured 
down  in  streams  through  the  ascending  current  of  air,  which  at 
the  time  is  too  strong  to  allow  even  the  largest  drops  to  fall  as 
rain. 

It  is  seen  from  a  reference  to  Table  VII  that  a  rain-drop  of 
0.2  inch  in  diameter  at  an  altitude  of  one  mile  cannot  fall 
through  an  ascending  current  of  air  with  a  velocity  of  25  miles 
per  hour;  and  those  with  still  smaller  diameters  are  carried  up 
to  where  the  velocity  and  density  are  such  that  they  are  sup- 
ported by  the  current,  and  begin  to  fall  only  after  they  become 
so  large,  or  the  velocity  of  the  ascending  current  becomes  so 
much  diminished,  that  they  are  no  longer  supported  in  the  air, 
and  fall  as  rain.  Hence  with  an  ascending  velocity  of  25  miles 
per  hour,  no  rain  in  drops  of  ordinary  size  of  0.2  inch  or  less  can 
fall  directly  back  to  the  earth ;  but  in  the  case  of  a  tornado  it  can 
be  carried  out  above,  and  fall  at  a  distance  from  the  centre, 
provided  the  drops  are  not  too  large  to  be  carried  up  above 
the  level  which  separates  the  lateral  inflowing  current  -below 
from  the  outflowing  current  above.  The  ascending  velocity 
may  be  such  as  to  carry  out  above  the  smaller  drops  only,  and 
those  with  larger  diameters  are  supported  in  the  cloud  in  the 
central  part  of  the  tornado  until,  by  blending  with  one  another, 
they  become  much  larger,  or,  in  the  case  of  very  rapid  ascend- 
ing currents,  until  they  collect  into  large  masses  which  force 
their  way  down  in  streams  of  water. 

281.  All  that  has  been  stated  with  regard  to  immense  rain- 
falls in  cloud-bursts  is  applicable,  with  a  few  modifications,  to 
the  sudden  falls  of  immense  quantities  of  hail.  In  this  case, 
however,  the  circumstances  must  be  such  that  the  out-turning 
current  is  at  a  great  altitude  and  the  strength  of  the  ascending 
current  is  so  great  that,  instead  of  the  accumulation  being 
down  very  far  below  the  region  of  freezing,  it  must  be  higher 
up,  but  not  necessarily  in  this  region.  For  the  hail-stones, 
formed  in  the  manner  described,  may  fall  directly  back  from 


434  TORNADOES. 

above,  or  be  carried  out  above  and  come  around  and  be  car- 
ried up  into  this  place  where  the  ascending  current  is  too 
strong  to  allow  them  to  fall,  and  not  strong  enough  to  carry 
them  up  where  the  current  above  would  carry  them  out  where 
they  can  fall,  and  so  they  remain  there  a  considerable  time 
without  much  loss  from  melting  even  when  collected  below 
the  region  of  freezing  temperature,  until  from  some  cause  the 
energy  of  the  tornado  becomes  exhausted  suddenly,  or  the 
accumulation  becomes  too  great  to  be  supported,  and  having 
once  broken  through  in  spots,  it  collects  together  into  streams, 
as  rain  does  in  a  cloud-burst,  and  falls  to  the  earth  in  a  very 
short  time,  leaving  a  great  depth  of  hail  over  a  short  and  very 
narrow  district  of  country. 

If  the  collection  of  hail  is  up  in  the  freezing-region,  then, 
by  the  continual  freezing  of  the  rain  carried  up  from  below  and 
coming  in  contact  with  the  hail-stones,  they  grow  until  they 
become  so  large,  or  until  the  velocity  of  the  current  is  so  much 
diminished,  that  they  can  be  no  longer  supported  in  the  air. 
This  may  not  be  until  they  become  very  large.  Accordingly, 
hail-stones  of  enormous  size  are  sometimes  observed,  and  even 
great  chunks  of  ice,  seemingly  formed  by  the  freezing  together 
of  the  water  and  the  hail-stones  collected  in  the  vortex  of  the 

tornado  (§  276). 

• 

FAIR-WEATHER  WHIRLWINDS  AND  WHITE  SQUALLS. 

282.  These  are  simply  small  tornadoes  which  occur  during 
fair  weather  whenever  and  wherever  the  proper  conditions  are 
found,  which  are  generally  when  there  is  an  unusually  rapid  de- 
crease of  temperature  with  increase  of  altitude,  or  else  a  very 
nearly  saturated  atmosphere.  They  are  sometimes  observed 
on  land,  but  mostly  on  lakes  and  at  sea,  and  may  be  accom- 
panied by  a  water-spout  or  not,  according  to  the  violence  of  the 
gyratory  motion  and  the  amount  of  aqueous  vapor  in  the  at- 
mosphere. At  first  a  small  cloud  is  formed  in  the  clear  sky, 
which  gradually  increases  from  the  condensation  of  vapor 
rapidly  carried  up  in  the  central  part  of  the  gyrating  and 


FAIR-WEATHER  WHIRLWINDS  AND   WHITE   SQUALLS.     435 

ascending  air  just  as  in  the  case  of  any  other  tornado.  The 
gyrations  may  sometimes  continue  to  increase  in  violence 
and  extent,  and  the  cloud  to  spread  until  it  assumes  the  dimen- 
sions of  a  tornado  such  as  usually  takes  place  in  a  cyclone ;  but 
it  is  mostly  confined  to  only  a  very  narrow  streak,  and  its  vio- 
lence, although  very  great  at  the  centre,  is  not  felt  at  a  short 
distance  away.  Although  the  gyrations  are  violent  very  near 
the  centre,  yet  decreasing  in  velocity,  at  least  a  little  above  the 
earth's  surface  where  the  friction  is  small,  somewhat  according 
to  the  law  expressed  in  §  42,  at  a  short  distance  from  the  centre 
they  are  entirely  harmless,  and  they  may  pass  very  near  with- 
out doing  any  injury.  If,  however,  they  pass  directly  over 
houses  on  land  or  a  ship  at  sea,  their  destructive  effects  may 
be  very  great  and  sudden. 

When  these  small  tornadoes  are  accompanied  by  a  water- 
spout and  are  first  seen  at  sea  at  a  distance,  they  can  generally 
be  avoided,  or,  if  not,  preparations  can  be  made  to  guard 
against  danger;  but  where  they  are  suddenly  formed  on  the 
spot  and  drop  down,  as  it  were,  from  above,  they  give  no  fore- 
warning of  approaching  danger.  A  remarkable  example  of 
this  kind  was  related  in  the  New  York  Herald  of  December  10, 
1878.  The  British  bark  Bel  Stuart,  Captain  Harper,  on  the 
•evening  of  November  14,  1878,  160  miles  from  Cape  Sable, 

•"  was  struck  by  a  white  squall  in  a  comparatively  smooth  sea  and  clear 
^ky.  which  swept  her  decks  and  created  consternation  on  board.  At  6 
P.M.  of  the  same  day,  all  hands  being  on  deck  after  supper,  a  strange 
sighing  of  the  wind  was  observed  by  the  watch,  and  the  sky  became  sud- 
denly threatening  without  corresponding  indication  of  the  barometer, 
which  showed  a  rising  tendency ;  Captain  Harper  and  his  first  officer  were 
on  the  deck  at  the  time.  All  hands  noticed  the  peculiar  change  in  sea 
and  sky,  and  were  discussing  it,  when,  without  a  moment's  notice,  the  sea 
forward  seemed  to  swell  up  to  meet  the  lowering  sky,  and  swept  the  bark 
•across  her  bows,  carrying  away  her  fore  top-gallant-mast,  jib,  jib-boom, 
foretop-mast  stays,  and  the  maintop-gallant-mast,  with  all  their  accom- 
panying sails.  In  a  moment,  as  it  seemed,  the  bark,  with  all  sail  set,  in  a 
fair  wind,  with  a  moderate  sea,  was  left  a  comparative  wreck  to  wallow 
in  the  trough  of  the  tremendous  seas  which  had  followed  the  spiral  vol- 
ume of  water.  Two  minutes  before  the  fatal  catastrophe,  Captain  Har- 
per says,  there  was  no  indication  of  the  water-spout." 


TORNADOES. 


It  seems  from  this  account  that  the  bark  ran  into  the  spout 
as  it  was  being  formed  and  before  it  became  visible.  The  sigh- 
ing of  the  wind  was  caused  by  the  rapid  gyrations  of  the  air, 
and  the  threatening  sky  by  the  incipient  condensation  of  the 
aqueous  vapors  carried  up  by  the  ascending  current.  The 
barometer,  before  its  very  near  approach,  remained  unaffected, 
because,  as  we  have  seen,  the  barometric  pressure  is  diminished 
only  at  and  very  near  the  centre,  and  it  was  by  this  that  the 
uprising  of  the  sea  was  caused  which  swept  across  the  bark. 

283.  When  we  have  the  conditions  of  a  water-spout  in  fair 
weather  with  little  moisture  in  the  air,  we  have  what  are  called 

white  squalls,  or  fair-weather  whirl- 
winds. In  such  cases  the  dew-point 
is  so  low,  and  consequently  the 
cloud,  when  formed,  is  so  high,  that 
the  gyrations  may  not  be  able  to 
bring  it  down,  in  the  form  of  a 
spout,  to  the  sea.  But  still  the 
gyrations  and  the  rapidly  ascending 
current  in  the  central  part  are  there, 
and  the  rising  and  boiling  of  the 
sea  below.  High  up  in  the  air  also, 
directly  over  the  boiling  of  the 
sea,  is  a  patch  of  white  cloud, 
formed  by  the  condensation  of  the 
vapor  in  the  ascending  current  when 
it  arrives  at  the  height  at  which  it 
begins  to  be  condensed.  This  cloud 
may  eventually  extend  over  a  con- 
siderable portion  of  the  heavens, 
but  at  first  it  is  a  small  cloud  in  a 
clear  sky,  as  represented  in  Fig.  12, 
and  is  white  because  of  the  great 
amount  of  reflected  light.  It  has 
no  doubt  the  funnel  shape  beneath, 
but  being  high  up,  and  the  observer  being  generally  near- 
ly under  it,  this  feature  is  hardly  ever  observed..  If  the 


Fig.  12. 


WHERE    TORNADOES  ARE  MOST  LIKELY   TO    OCCUR.     437 

air  be  not    too   dry,    it   may   be    followed    by   a    shower   of 
rain. 

Peltier  says : 

"  White  squalls  are  very  rare,  but  they  are  sometimes  met  with  be- 
tween the  tropics,  especially  near  elevated  lands.  They  are  generally 
violent  and  of  short  duration.  They  often  take  place  when  the  sky  is 
clear,  and  without  any  atmospheric  circumstances  giving  notice  of  their 
approach.  The  only  thing  which  indicates  their  proximity  is  the  boiling 
of  the  sea,  which  is  very  much  agitated  by  the  violence  of  the  winds. 
Many  of  these  squalls,  which  commence  by  a  little  cloud,  or  even  with- 
out any  visible  cloud,  are  soon  accompanied  by  violent  rains  and  thick 
clouds." 

On  the  west  coast  of  Africa  these  little  tornadoes  or  whirl- 
winds are  called  bull's-eye  squalls.  According  to  Piddington, 
the  Portuguese  describe  such  a  squall  as  "  first  appearing  like  a 
bright  white  spot  at  or  near  the  zenith,  in  a  perfectly  clear  sky 
and  fine  weather,  and  which,  rapidly  descending,  brings  with  it 
a  furious  white  squall  or  tornado." 

From  the  preceding  description  it  is  evident  that  these 
squalls  differ  but  little  in  their  nature  from  the  small  tornadoes 
and  water-spouts  met  with  in  higher  latitudes,  such  as  the  one 
which  nearly  wrecked  the  bark  Bel  Stuart,  except  that  the  at- 
mosphere is  usually  too  dry  for  the  formation  of  a  water-spout. 

WHERE  TORNADOES  ARE  MOST  LIKELY  TO   OCCUR. 

284.  It  has  been  shown  that  there  are  two  principal  condi- 
tions upon  which  tornadoes  depend,  and  that  in  the  absence  of 
either  of  these  they  cannot  take  place.  The  one  is  the  state 
of  unstable  equilibrium  of  the  air,  and  the  other  a  gyratory 
motion  with  reference  to  any  assumed  centre.  It  is  not  neces- 
sary that  the  centre  shall  be  stationary,  but  simply  that  the 
motion  of  the  air  around  it  shall  be  such  that,  when  it  is  drawn 
in  toward  this  centre,  it  shall  run  into  a  gyration  around  it. 
When  we  have  these  two  principal  conditions,  the  other,  that 
that  there  shall  be  some  slight  initial  disturbance  to  cause  the 
air  to  burst  up  at  some  point  through  the  strata  above,  can 
scarcely  ever  be  wanting.  The  places  and  times,  then,  in  which 


438  TORNADOES. 

these  two  principal  conditions  are  found  are  those  in  which 
tornadoes  are  most  likely  to  occur.  Of  these  two,  however,, 
the  unstable  equilibrium  is  the  most  important,  since  it  more 
rarely  occurs  than  the  other,  which  is  scarcely  ever  so  entirely 
absent  as  not  to  give  at  least  some  gyratory  motion  which  be- 
comes violent  very  near  the  centre. 

285.  With  regard  to  fixed  areas  on  the  earth's  surface 
where  the  unstable  state  is  most  readily  induced  at  all  seasons 
of  the  year,  these  are  found  where,  in  the  general  motions  of 
the  atmosphere  as  deflected  by  continents  and  mountain 
ranges,  currents  of  air  at  the  earth's  surface  which  come  from 
a  warmer  latitude,  or  at  sea  from  a  much  warmer  continent,  are 
caused  to  flow  under  the  cold  upper  strata  where  the  normal 
motion  is  nearly  eastward,  and  where  consequently  the  temper- 
ature is  the  normal  one,  not  affected  by  such  motion  as  takes 
place  in  the  lower  strata.  One  such  place  is  found  in  the  Mis- 
sissippi Valley,  and  especially  between  the  Mississippi  and  the 
Rocky  Mountain  range,  where  the  air  currents  of  the  lower 
strata  are  from  lower  latitudes,  comprising  the  Gulf  of  Mexico^ 
curving  around  first  northward  and  then  more  eastwardly  under 
the  higher  upper  strata  which  pass  over  the  top  of  the  range 
of  the  Rocky  Mountains,  and  directly  or  nearly  eastward  with- 
out having  their  temperatures  changed  from  the  normal  tem- 
perature of  the  latitude  by  such  deflections..  And  this  is  espe- 
cially the  case  in  the  summer  season,  when  the  interior  of  the 
continent  is  warmed  up  and  the  air  of  the  lower  strata  is 
drawn  from  lower  latitudes  far  up  into  the  higher  latitudes  on 
the  eastern  side  of  the  Rocky  Mountains,  and  the  isothermal 
curve  there  is  deflected  very  far  toward  the  north.  From  this 
cause  the  temperature  of  the  lower  strata  of  this  region  be- 
comes unusually  great  relatively  to  that  of  the  strata  above ; 
and  if  the  complete  unstable  state  is  not  induced  from  this 
alone,  it  is  readily  brought  about  by  the  addition  of  any  small 
effect  from  some  other  cause,  as  from  extremely  warm  weather 
in  which  the  earth's  surface  and  the  lower  air  strata  become 
abnormally  heated.  The  great  moisture  of  the  air  in  these 
southerly  winds  is  also  favorable  to  the  induction  of  the  un- 


WHERE    TORNADOES  ARE  MOST  LIKELY   TO   OCCUR.     439 

stable  state,  since  this  state  is  more  readily  brought  about  in  air 
nearly  or  quite  saturated. 

286.  The  other  condition  of  tornadoes,  that  of  a  relative 
gyratory  motion  with  regard  to  any  point,  is  also  found  to  an 
unusual  extent  in  this  region,  especially  in  the  winter  season. 
For  the  southerly  current  curving  around  toward  the  east 
causes  a  pressure  toward  the  right,  giving  rise  to  the  perma- 
nent barometric  gradient  of  increasing  pressure  toward  the 
central  part  of  the  permanent  area  of  high  pressure  in  the 
Atlantic  Ocean  east  of  Florida ;  and  on  account  of  this  there  is 
a  counter-current  between  this  and  the  Rocky  Mountains,  flow- 
ing down  toward  Texas,  just  as  in  the  Atlantic  Ocean  the 
Greenland  current  flows  down  to  Florida  between  the  Gulf 
Stream  and  the  coast  of  the  United  States.  There  is  evidence 
of  such  a  current  in  this  region  in  the  averages  of  all  seasons 
since  the  resultant  of  these  has  a  large  southerly  component, 
and  especially  is  this  seen  in  the  isotherms  of  the  Mississippi 
Valley  extending  in  a  somewhat  northeasterly  and  southwest- 
erly direction,  so  that  the  mean  temperature  of  New  Mexico 
and  the  northern  part  of  Texas  is  the  same  as  that  of  places 
east  of  the  Mississippi  from  five  to  ten  degrees  farther  north. 
In  the  summer  season  this  flow  of  cold  air  down  toward  the 
Gulf  is  confined  to  a  comparatively  narrow  belt  close  to  the 
mountain  range;  for  then  the  warm  currents  from  the  Gulf  are 
drawn  farther  up  toward  the  northwest.  At  this  season  the 
northern  part  of  Texas  has  the  same  mean  temperature  as 
Minnesota,  and  the  isotherms  are  nearly  north  and  south  in  di- 
rection, and  the  contrast  between  the  temperature  of  the  warm 
southerly  winds  on  the  one  side,  and  the  colder  northerly  ones 
on  the  other  side,  is  similar  to  that  of  the  cold  wall  between 
the  Gulf  Stream  and  Greenland  current  in  the  Atlantic  Ocean. 
This  tendency  of  the  air,  therefore,  to  flow  in  contrary  direc- 
tions gives  the  second  condition  of  a  tornado  to  a  greater  de- 
g^ee  in  this  region  than  in  almost  any  other.  Both  of  the  two 
principal  conditions  of  tornadoes,  therefore,  are  found  in  a  pre- 
eminent degree  in  the  Mississippi  Valley,  and  especially  be- 
tween the  Mississippi  and  the  Rocky  Mountains.  Hence  there 


440  TORNADOES. 

is  perhaps  no  part  of  the  world  where  they  prevail  more  than 
in  this  region,  and  especially  in  that  part  of  it  in  the  middle 
latitudes  west  of  the  Mississippi  River  embracing  Kansas  and 
Missouri. 

Near  the  Rocky  Mountain  range,  and  some  distance  to  the 
east  of  it,  the  conditions  are  not  so  favorable,  both  on  account 
of  the  dryness  and  the  lower  temperature  of  the  air.  Hence 
in  this  region  large  destructive  tornadoes  do  not  prevail  much, 
though  small  tornadoes  with  water-spouts  are  of  frequent  occur- 
rence in  the  lower  strata  of  the4  atmosphere. 

287.  Another  place  on  the  globe  where  the  normal  condi- 
tion of  the  atmosphere  approximates  to  the  unstable  state  is 
on  the  west  coast  of  Africa  and   extending  a  considerable  dis- 
tance westward  over  the   ocean.     Here  the  warm  trade-winds 
from  the  northern  part  of  Africa  run  under  the  comparatively 
very  cold  air  of  the   upper  strata,  moving  eastward   over  the 
Atlantic,  and  thus  causes  a  very  rapid  decrease  of  temperature 
with  increase  of  altitude,  very  nearly,  if  not  quite  equal  to  that 
which  produces  the  unstable  state  in  unsaturated  air.     But  the 
excessive  dryness  of  the  air  here,  coming  from  the  coast  of 
Africa,  is  a  condition  which  is  not  favorable  to  the  formation  of 
large  tornadoes  accompanied  by  water-spouts,  but  very  small 
tornadoes  or  whirlwinds  without   spouts,  usually  called  white 
squalls,  are  very  frequently  seen  in  this  region  and  are  here 
called  bull's-eye  squalls. 

288.  For  well-known   reasons,  the   unstable   state   occurs 
mostly  in  the  cloud   region,  and  hence   the  tornadic  gyrations 
usually  commence  there   first,  and  are  afterwards  propagated 
downward  to  the  earth's  surface.     The  unstable  state,  however, 
is  often  produced  in  the  lower,  unsaturated  strata  of  the  atmos- 
phere,  even  when  very  dry;  and  then  if  the  other  condition 
of  a   tornado    is   present,    small    tornadoes   at   least    may   be 
formed,  even  where  this  unstable  state  does  not  extend  to  the 
upper  strata,  and  thus  tornadoes  occur  not  only  in  cyclones, 
but  elsewhere  and  in  clear  weather.     In  such  cases,  however, 
the  effects  do  not  reach  very  high  into  the  atmosphere. 

The  unstable  state  in  unsaturated  air  occurs  mostly  on  very 


WHERE    TORNADOES  ARE  MOST  LIKELY   TO   OCCUR.     44* 

•dry  and  sandy  soils,  with  little  heat  conductivity,  when  the 
weather  is  very  warm  and  the  heat  rays  of  the  sun  are  un- 
obstructed by  any  clouds  above.  The  heat  thus  accumulates 
in  the  surface  strata  of  the  soil  and  the  lower  strata  of  the 
atmosphere,  and  thus  is  brought  about  the  unstable  state,  at 
least  up  to  a  low  altitude,  even  in  clear  and  dry  weather. 

The  same  is  often  found,  also,  in  very  calm  weather  over 
the  surface  of  seas  and  lakes.  The  surface  of  the  water  be- 
comes heated,  and  also  the  lower  strata  of  the  atmosphere,  by 
heat  rays  passing  directly  down  and  by  those  reflected  back 
until  the  unstable  is  brought  about. 

289.  The  season  of  the  year  in  which  tornadoes  mostly 
occur  is  that  in  which  the  atmosphere  in  its  normal  state  for 
the  season  approaches  most  nearly  the  unstable  state.     This 
seems  to  be  in  all  parts  of  the  world  in  the  summer  season,  and 
in  the  United  States  at  least  in  the  early  part  of  summer,  May 
or  June.     Hence,  although  tornadoes  occur  at  all  seasons  and 
in  every  month  of  the   year,  yet,  according   to   Finley's   re- 
searches,73 "  summer  is  the  season  of  greatest  frequency,"  and 
"  June  is  the  month  in  which  they  occur   most  frequently." 
The   relative  frequency   of   their   occurrence    in   the    United 
States  during  the  winter,  spring,  summer,  and  fall  seasons  was 
found  to  be  respectively  as  the  numbers  35,  215,  240,  and  86. 
These  numbers  indicate   a  great  difference  between  summer 
and  winter  in  the  frequency  of  their  occurrence,  and  also,  since 
the  numbers  for  spring  and  summer  do  not  differ  much,  that 
the  maximum  occurs  very  early  in  the  summer. 

290.  For  the  very  same  reason  that  tornadoes  occur  mostly 
during  the  warmest  season   of  the  year  and  very  rarely  in  the 
winter  season,  they  should   occur  during  the  warmest  part  of 
the  day  and  seldom  at  night.     For  during  the  day  the  surface 
of  the  earth  and  the  lower  strata  become  very  much  warmed 
up,  and  at  night  the  reverse  takes  place  from  nocturnal  cooling, 
while  the  temperature  at  a  moderate  elevation  is  subject  to 
only  a  small  diurnal  variation.     Hence,  when  the  general  state 
of  the   atmosphere,  aside  from  its   diurnal  variation,  is  very 
mearly  that  of  the  unstable  state,  this  state  is  frequently  induced 


442  TORNADOES. 

during  the  warmest  part  of  the  day  by  this  diurnal  and  other, 
abnormal  variations,  but  very  rarely  at  night.  Accordingly 
Finley  found  that  "  tornadoes  are  most  frequent  in  the  after- 
noon between  noon  and  6  o'clock,"  and  that  "  the  hour  during 
which  the  greatest  number  of  tornadoes  occurred  was  from 
5  to  6  P.M.,"  and  that  "  the  next  hour  was  from  4  to  5  P.M." 

The  same  is  true  with  regard  to  small  tornadoes  and  water- 
spouts, as  well  as  those  which  occur  in  cyclones.  M.  Defranc77 
remarks  that  he  "never  saw  a  water-spout  before  10  o'clock  in, 
the  morning  nor  after  5  o'clock  in  the  evening,"  that  "  they 
never  appear  during  the  night  nor  during  the  winter,  and  that 
there  are  always  two  circumstances  attending  them :  the  first 
is  the  presence  of  the  sun  during  or  a  little  before  the  phe- 
nomenon ;  the  second  is  the  absence  of  the  wind,  or  only  a 
very  feeble  one,  except  in  the  space  occupied  by  the  water- 
spout." 

This  refers  mostly  to  small  water-spouts  on  seas  and  lakes,, 
depending  upon  the  conditions  referred  to  in  a  preceding 
paragraph. 

291.  Tornadoes  occur  mostly  in  the  summer  season  and 
during  the  warmest  part  of  the  day,  not  only  because  the 
vertical  gradient  of  decreasing  temperature  is  greatest  at  these 
times,  but  also  because  a  smaller  gradient  is  required  to  induce 
the  unstable  state  then  than  during  the  coldest  season  of  the 
year  and  the  coldest  part  of  the  day.  By  referring  to  Table 
III,  Appendix,  it  is  seen  that  with  a  hot  surface  temperature 
of  the  air  during  the  warmest  part  of  the  day  in  the  summer 
season,  say  35°,  the  unstable  state  for  saturated  air  is  induced 
with  a  vertical  gradient  of  decreasing  temperature  of  0.35°  for 
each  100  meters,  while,  if  the  temperature  were  that  of  freez- 
ing, the  gradient  would  have  to  be  0.63°  for  each  100  meters, 
and  Jience  nearly  twice  as  great  as  in  the  former  case.  So 
great  a  gradient  as  the  latter  is  rarely  if  ever  found  in  winter, 
even  during  the  warmest  part  of  the  day. 

In  the  case  of  small  fair-weather  tornadoes  and  water- 
spouts, such  as  are  observed  on  seas  and  lakes,  unless  the 
atmosphere  is  very  near  the  point  of  saturation,  the  vertical 


SAND-SPOUTS  AND  DUST    WHIRLWINDS.  445 

temperature  gradient  required  is  very  nearly  that  of  dry  air,, 
which  is  never  found  in  the  winter  season,  and  only  during  the 
hottest  part  of  the  day  in  summer.  Hence  these  are  never 
observed  at  night  even  in  the  summer  season. 

292.  Where  the  unstable  state  has  been  very  nearly  induced 
from    some   other  cause,  as  a  very   hot  surface  temperature 
during  a  warm,  clear  day,  it  may  often  be  consummated  by  the 
burning  of  dry  brush  on  the  earth's  surface,  or  of  a  cane-brake,, 
or  by  a  large  fire  of  any  sort,  and  thus  great   whirlwinds,  and 
even  showers  of  rain  accompanied  with  thunder,  may  be  pro- 
duced.    The  vertical  columns  often  visible  in  such  cases  are 
composed  of  dark  smoke  brought  in  from  all  sides,  and  carried 
up  in  the  centre.     These  assume  all  the  usual  forms  of  water- 
spouts, and  of  course  often  contain  also  condensed  vapor  in  the 
form  of  a  water-spout,  concealed  by  the  smoke,  else  rain  would 
not  be  produced. 

Mr.  Olmsted "  has  given  an  interesting  account  of  such 
phenomena  arising  from  the  burning  of  a  cane-brake  on  the 
shores  of  the  Black  Warrior,  in  Alabama.  Columns  of  smoke 
of  various  forms  were  witnessed,  which  assumed  the  usual 
forms  of  water-spouts,  some  extending  up  to  only  a  moderate 
height  with  a  funnel  shape  at  the  top,  while  others  were  very 
slender  columns  extending  up  300  yards  into  the  clouds  of 
smoke,  and  all  were  accompanied  with  a  whirling  motion  of 
the  air  and  the  smoke.  Both  Redfield  88  and  Espy34  have  given 
a  number  of  statements  made  by  eye  witnesses  of  the  effects 
of  great  fires  in  producing  whirlwinds,  rain,  and  thunder,  from 
which  it  appears  evident  that  they  are  at  times  followed  by  a 
considerable  amount  of  rain.  And  it  was  proposed  by  the 
latter  to  try  the  experiment  of  producing  artificial  rains  in  time 
of  drought  by  burning  great  quantities  of  brush-wood,  or  by 
means  of  prairie  fires  in  the  West  when  the  grass  is  dry. 

SAND-SPOUTS   AND   DUST  WHIRLWINDS. 

293.  In  very  hot,  dry  climates,  where  there  is  a  sandy  soil,, 
sand-spouts   and    dust   whirlwinds  are  of  frequent  occurrence^ 


444  TORNADOES. 

The  dry  air  of  such  climates,  especially  over  a  sandy  soil,  is 
often  in  a  state  of  unstable  equilibrium  from  the  accumulation 
of  heat  on  the  earth's  surface,  for  a  sandy,  dry  soil  conducts  it 
very  slowly  down  into  the  earth,  and  there  are  then  generally 
all  the  conditions  of  a  whirlwind  and  a  water-spout,  except 
the  vapor  in  the  air  to  condense,  for  the  condition  of  an  initial 
whirl  of  the  air  can  scarcely  ever  be  wanting  where  there  is  not 
a  perfect  calm.  The  gyrations  of  the  air  and  the  ascending 
currents  are  the  same  as  in  a  water-spout,  but  instead  of 
aqueous  vapor,  sand  or  dust  collected  and  drawn  in  from  the 
vicinity  is  carried  up.  The  inflowing  and  spiral  currents  from 
all  sides  towards  the  vortex,  up  to  a  considerable  height  often, 
keep  it  near  the  centre  in  the  form  of  a  column  or  pillar  of 
sand,  if  the  whirlwind  is  well  developed  over  a  small  area 
only,  with  very  rapid  gyrations  and  a  strong  ascending  current. 
The  height  of  the  column  depends  upon  the  strength  of  the 
ascending  currents  and  the  altitude  at  which  they  are  turned 
outward  from  the  vortex ;  for,  as  in  cyclones  and  water-spouts, 
where  there  is  a  flowing  of  the  air  in  from  all  sides  below,  it 
must  flow  out  again  above  a  certain  altitude,  depending  upon 
the  different  circumstances  under  which  the  whirlwind  takes 
place.  Sand-spouts  are  frequently  observed  in  Arabia,  Persia, 
and  India,  and  also  in  Arizona  and  other  places  in  the  western 
part  of  the  United  States,  where  the  climate  is  very  dry.  In 
the  hot,  dry  climate  of  Australia,  situated  in  the  dry  zone  of 
the  southern  hemisphere,  these  pillars  of  sand  are  said  to  be 
often  more  than  a  half-mile  in  height. 

Humboldt,  in  his  "  Aspects  of  Nature,"  refers  to  the  sand- 
spouts during  the  dry  season  on  the  Orinoco,  South  America, 
and  says  that  "  like  conical-shaped  clouds,  the  points  of  which 
•descend  to  the  earth,  the  sand  rises  through  the  rarefied  air  on 
the  electrically  charged  centre  of  the  whirling  current,  resem- 
bling the  loud  water-spout,  dreaded  by  the  experienced  mar- 
iner" (§  119).  He  seems  to  think,  however,  that  electricity 
has  something  to  do  with  the  phenomena. 

Where  the  whirls  take  place  over  a  considerable  area,  and 
do  not  become  concentrated  into  rapid  gyrations  near  the 


SAND-SPOUTS  AND   DUST   WHIRLWINDS.  44$ 

centre,  and  the  ascending  currents  do  not  extend  up  very  high, 
they  give  rise  to  dust  whirlwinds,  which  often  overtake  caravans 
and  travellers  in  the  deserts ;  and  if  they  produce  no  fatal 
effects,  they  are  at  least  very  unpleasant  and  annoying.  These 
are  very  frequent  in  India  and  the  Sahara,  or  Great  Desert  of 
northern  Africa,  and  in  fact  in  all  places  in  the  warmer  lati- 
tudes where  there  is  a  dry,  sandy  soil. 

When  the  air  is  nearly  calm,  the  sand  and  a  thin  stratum  of 
atmosphere  in  contact  with  it  become  heated  very  much  above 
the  ordinary  temperature  of  the  air  a  little  above  the  surface. 
The  inflowing  currents  of  the  whirlwind  from  all  sides  collect 
this  warm  surface  stratum  into  the  central  part  of  the  whirl- 
wind and  cause  the  whole  interior  to  be  of  an  extraordinarily 
high  temperature.  The  much-dreaded  simoom,  stripped  of  all 
exaggerations,  is  most  probably  simply  one  of  these  dust  whirl- 
winds. 

294.  Sand-spouts,  as  well  as  water-spouts,  have  been. ob- 
served to  be  hollow.  Of  a  whirlwind  observed  at  Schell  City, 
Mo.,  in  the  summer  of  1879,  ^  was  sa^  :H> 

"  There  were  no  suface  winds  strong  enough  to  bear  dust  along  the 
surface  of  the  ground,  but  the  dust  carried  up  in  the  vortex  was  collected 
only  at  the  vortex  of  the  whirl.  The  dust  column  was  about  two  hun- 
dred feet  high,  and  perhaps  about  thirty  or  forty  feet  in  diameter  at  the 
top.  The  direction  of  rotation  was  the  same  as  of  storms  in  the  northern 
hemisphere.  Leaving  the  road,  the  whirl  passed  out  on  the  prairie,  im- 
mediately filling  the  air  with  hay,  which  was  carried  up  in  somewhat 
wider  spirals,  the  diameter  of  the  cone  thus  filled  with  hay  being  about 
one  hundred  and  fifty  feet  at  the  top.  It  was  then  observed  also  that 
the  column  was  hollow.  Standing  nearly  under  it,  the  bottom  of  the 
dust  column  appeared  like  an  annulus  of  dust  surrounding  a  circular 
area  of  perfectly  clear  air.  The  area  grew  larger  as  the  dust  was  raised 
higher,  being  about  fifteen  or  twenty  feet  wide  when  last  observed." 

The  sand-spout  and  the  dust  whirlwind,  where  well  devel- 
oped and  concentrated,  are  free  from  sand  or  dust  in  the  centre, 
for  the  same  reason  that  the  water-spout  is  free  from  cloud  or 
condensed  vapor.  The  centrifugal  force  of  the  gyrations  keeps 
it  off  at  a  distance  where  this  force  is  just  equal  to  that  of  the 
indrawing  currents  which  tend  to  drive  it  in  toward  the  vortex- 


446  TORNADOES. 


BLASTS     OF   WIND    AND    OSCILLATIONS    OF    THE    WIND-VANE. 

295.  The  wind  is  often  observed  to  blow  in  blasts,  with  an 
oscillating  vane  and  unsteady  barometer.  This  arises  from 
the  air  running  into  numerous  whirls,  or  gyrations,  while  it  at 
the  same  time  has  a  progressive  motion.  As  in  a  cyclone, 
while  passing  over  any  place,  the  wind  is  first  from  one  direc- 
tion and  then,  in  the  course  of  a  day  or  two,  gradually  veers 
around  to  another,  often  to  one  in  nearly  a  contrary  direction, 
so,  in  the  passages  of  small  whirlwinds,  the  vane  in  like  manner 
oscillates  from  one  direction  to  another  in  a  few  minutes,  the 
manner  and  range  of  oscillation,  as  in  the  case  of  a  cyclone, 
depending  upon  which  side  of  the  vane  the  centre  of  the  whirl 
passes,  and  the  distance  from  it.  If  the  centre  of  the  whirl 
passes  over  the  vane,  then  there  is  a  very  sudden  oscillation  of 
the  vane  through  a  range  of  180°,  or  nearly,  especially  where 
the  diameter  of  the  whirling  air  column  is  small. 

As  in  a  cyclone  the  velocity  of  the  wind  is  the  greatest  on 
the  side  called  the  dangerous  side,  on  which  the  direction  of 
cyclonic  motion  coincides  with  that  of  the  general  progressive 
motion,  and  is  comparatively  small,  or  may  entirely  vanish,  on 
the  opposite  side,  so  in  one  of  these  small  whirls  of  air  the 
velocity  on  the  one  side  is  very  much  increased  above  the 
average,  which  is  that  of  the  general  progressive  motion,  while 
on  the  other  it  is  much  diminished,  and  there  may  be  almost  a 
calm.  Wherever  the  air  is  in  the  unstable  state  these  little 
whirls  are  very  numerous,  and  consequently,  in  their  passage 
over  any  place,  they  cause  the  wind  to  blow  in  blasts,  and  a 
very  frequent  oscillation  of  the  vane  from  side  to  side  occurs, 
sometimes  from  right  to  left,  and  at  other  times  in  the  contrary 
way. 

These  little  whirls  in  the  atmosphere  are  especially  liable  to 
occur  in  connection  with  cyclones  extending  over  a  consider- 
able area ;  for  in  these,  especially  up  in  the  cloud  region,  the 
air  is  in  the  unstable  state,  and,  on  account  of  the  gyrations  of 
the  cyclone  and  the  general  agitation  of  the  air,  the  sum  of  the 


OSCILLATIONS  OF   THE    WIND-VANE.  447 

moments  of  gyration,  with  regard  to  any  point  where  there  is  a 
rushing  up  of  the  air  of  the  lower  strata  through  those  above, 
can  scarcely  ever  be  o,  and  hence  there  are  both  of  the  two 
principal  conditions  of  such  little  whirlwinds.  These  may  form 
small  secondary  cyclones  contained  within  the  larger,  or  tor- 
nadoes and  water-spouts,  or  simply  local  whirlings  in  the 
atmosphere  of  small  extent  and  no  great  violence,  but  suffi- 
cient to  cause  intermittences  in  the  steadiness  of  the  velocity 
of  the  wind  and  oscillations  in  its  general  direction.  Hence 
there  is  generally  great  unsteadiness  in  the  velocity  and  direc- 
tion of  the  wind  in  a  cyclone,  and  the  greatest  injuries  usually 
arise  from  the  violence  of  the  wind  on  the  side  of  these  sub- 
sidiary whirls  where  the  direction  of  motion  coincides  with  that 
of  the  gyratory  motion  of  the  cyclone. 

These  blasts  and  oscillations  of  the  vane  are  generally  ob- 
served on  the  clearing-up  side  of  a  storm.  As  the  central  area 
•of  a  cyclone  is  warmer  than  the  surrounding  parts,  and  the 
upper  colder  strata  in  middle  and  higher  latitudes  move  east- 
ward faster  than  the  lower  strata,  the  effect  is  to  cause  a  more 
rapid  decrease  of  temperature  with  increase  of  altitude,  and 
hence  to  induce  the  unstable  state  which  gives  rise  to  these 
whirls.  As  the  air  is  comparatively  dry  on  this  side  of  the 
storm,  the  small  amount  of  vapor  remaining  is  usually  carried 
up  in  the  central  part  of  the  whirl  to  a  considerable  altitude 
fcefore  condensation  takes  place,  and  then  it  forms  a  patch  of 
-whitish  fracto-cumulus  cloud  of  greater  or  less  extent,  or  even 
.sometimes  to  a  large  dark  cloud  if  the  extent  and  duration  of 
the  whirlwind  are  sufficiently  great.  As  the  condensed  vapor 
is  carried  up  in  the  shape  of  a  cumulus  cloud  to  a  considerable 
height  above  its  base,  and  the  progressive  velocity  of  the  upper 
strata  is  greater  than  that  of  the  lower,  the  tops  are  blown 
forward  in  the  general  direction  of  the  currents,  so  that  they 
often  appear  of  an  oblong  shape  and  indicate  the  general 
direction  of  the  currents  at  that  altitude.  Such  clouds  usually 
appear  for  a  while  and  gradually  vanish  by  the  re-evaporation 
of  the  condensed  vapor  forming  them. 


448  TORNADOES. 


"  PUMPING  "    OF   THE   BAROMETER. 

296.  In  connection  with  frequent  changes  of  the  velocity, 
and  consequently  force,  of  the  wind,  there  is  an  unsteadiness  of 
barometrical  column  called  "  pumping,"  where  the  barometer 
is  placed  on  one  side  or  the  other  of  a  barrier  to  the  progress 
of  the  air.  This  effect  is  given  in  millimeters  of  the  barome- 
ter by  the  formula  of  §  235.  According  to  this,  where  the 
barometer  is  placed  against  a  wall  or  post  where  the  wind 
blows  normally  against  its  surface  with  a  velocity  of  10  meters 
per  second,  the  height  of  the  barometer  is  increased  0.5 
mm.  If  the  velocity  is  increased  to  20  m.  per  second,  it  becomes 
2.0  mm.,  and  hence  a  change  of  1.5  mm.  with  a  change  of 
velocity  from  10  m.  to  20  m.  per  second.  With  a  change, 
however,  from  20  m.  to  30  m.  per  second  the  change  in  baro- 
metric pressure  would  be  2.5  mm.  Hence  the  same  change  of 
velocity  where  the  velocity  is  already  great  gives  a  much 
greater  effect  upon  the  barometer  than  the  same  change  in 
velocity  where  the  velocity  as  yet  is  small.  Hence  in  cyclones 
where  the  general  velocity  is  great,  small  changes  in  velocity 
produce  a  considerable  effect  on  the  barometer ;  and  it  is  in 
cyclones,  therefore,  where  this  effect  is  mostly  observed. 
Much  depends  upon  the  position  of  the  barometer.  If  placed 
in  the  open  air,  little  or  no  effect  is  observed,  since  there  is 
little  obstruction  to  the  wind.  If  placed  where  wind  blows 
obliquely  against  the  face  of  the  barrier,  the  value  of  AP  in 
the  formula  must  be  multiplied  by  cos2  /',  i  being  the  angle 
of  incidence  of  the  wind,  and  hence  the  effect  is  diminished 
proportionally.  On  the  lee  side  of  a  barrier  there  is  a  slight 
depression  of  the  barometer  with  the  increase  of  velocity  in 
the  blasts  arising  from  the  dragging  away  of  the  air  on  that 
side  through  friction.  A  barometer  placed  in  a  tight  room,  of 
course,  cannot  be  much  affected,  and  perhaps  not  sensibly  in 
any  room  with  doors  and  windows  closed,  especially  when  the 
blasts  are  sudden  and  of  so  short  duration  that  there  is  not 
time  for  the  increase  of  pressure  to  be  felt  inside. 


"PUMPING"   OF   THE  BAROMETER.  449 

In  the  hurricanes  of  the  Antilles,  observation  shows  that 
these  small  oscillations  of  the  barometer  are  closely  connected 
with  and  dependent  upon  the  blasts  of  the  wind,  and  that 
oscillations  of  the  vane  always  accompany  the  blasts,  showing 
that  the  latter  are  due  to  small  gyrations  of  the  air.  Padre 
Vifles  says : 

"  Under  the  influence  of  the  blasts,  the  barometric  column  is  so  agi- 
tated and  so  irregular  that  it  renders  the  reading  of  it  very  difficult, 
since  it  is  scarcely  possible  to  take  an  exact  medium.  The  amplitude 
of  the  oscillations  is  usually  from  four  to  eight  tenths  of  a  millimeter, 
and  sometimes  more.  The  agitation  is  fitful  and  violent,  just  as  the 
impulses  which  the  anemometer  receives  and  the  oscillations  made  by 
the  vane." 


CHAPTER  VIII. 

THUNDER-STORMS. 

297.  THE  greater  part  of  violent  tornadoes  are  accompanied 
by  thunder,  and  so  are  properly  called  thunder-storms.     Ac- 
cording to  Finley,  "  of  473  cases  in  which  the  atmospheric  con- 
(iitions  preceding  tornadoes  were  observed,  410  were  reported 
as   violent    thunder-storms."     But    usually  in    thunder-storms 
there  is  little  of  either  cyclonic  or  tornadic  violence,  and  the 
wind  accompanying  them,  when  strong,  is  more  of  the  character 
of  a  sudden  and  violent   squall,  though  it  often  amounts  to 
nothing  more  than  a  gentle  wind  blowing   out  beneath   the 
thunder-cloud. 

Much  attention  has  been  given  of  late  years  to  the  study  of 
thunder-storms,  both  in  the  principal  countries  of  Europe,  and 
by  the  Signal  Service  and  the  New  England  Meteorological 
Society  of  our  country.  The  principal  results  obtained  in 
these  studies,  from  very  numerous  observations  by  M.  Fron  in 
France,  Ferrari  in  Italy,  Von  Bezold  in  Bavaria,  Assmann  in 
Germany,  Mantel  in  Switzerland,  Klossovsky  in  Russia,  Elliot 
in  India,  and  Mohn  in  Norway,  have  been  given  briefly  by 
Professor  W.  M.  Davis.80  He  has  also  given  a  report  on  the 
thunder-storms  in  New  England  in  the  summer  of  1885."  To 
these  contributions  on  the  subject  the  writer  is  indebted  mainly 
for  the  facts  in  what  follows  on  this  subject. 

OBSERVED    PHENOMENA. 

298.  Thunder-storms  often  appear  to  be  small  and  imper- 
fectly developed  cyclones  in  which  there  is  little  or  no  sensible 
gyratory  motion  or  barometric  depression.     Klossovsky  regards 
them  as  small  cyclones  originating  in  certain  segments  near  the 

450 


OBSERVED   PHENOMENA.  45  1 

periphery  of  larger  cyclones.  According  to  Abercromby, 
thunder-storms  are  always  connected  with  secondary  cyclones. 
He  says  :50 

"As  surely  as  we  see  a  secondary  on  the  charts  in  summer,  so  cer- 
tainly will  thunder-storms  occur  during  the  day,  though  we  cannot  say 
in  what  portion  of  the  small  depression." 

Again : 

"  As  the  secondary  approaches  any  station,  the  wind  draws  more  or 
less  in  toward  the  centre,  and  recovers  its  former  direction  after  the  de- 
pression has  passed." 

In  central  Germany  also 

"  The  wind  in  thunder-storms  veers  and  backs  with  equal  frequency ; 
and  not  unfrequently  reverses  its  course  directly." 80 

In  one  of  the  local  thunder-storms  of  July  29,  1885,  in  New 
England,  there  were  indications  of 

"  a  tolerably  distinct  cyclonic  motion  of  the  winds  within  and  around  the 
oval  rain-area,  implying  that  the  thunder-storm  area  possessed  a  gentle, 
spiral,  rotary  circulation  on  a  small  scale,  as  has  been  determined  for 
.storms  of  this  kind  in  Europe."81 

In  Italy  it  is  said  :80 

"The  storms  occur  on  the  after-side  of  a  small,  faint  area  of  low  pres- 
.sure ;  and  that  the  pressure  rises  as  the  maximum  phase  of  the  storm 
approaches.  .  .  .  Sometimes  the  storms  form  at  the  end  of  a  V-shaped 
"  sack'  or  enlargement  on  the  side  of  a  large  area  of  low  pressure." 

And  in  Bavaria : 

"On  maps  having  the  pressure  shown  from  five  to  five  milli- 
meters, the  areas  of  low  pressure  are  but  faintly  indicated  by  curves  in 
the  isobars  ;  with  more  detailed  study,  they  appear  in  greater  distinct- 
ness and  are  generally  seen  to  be  extensions  of  larger  low-pressure  areas, 
with  gradients  so  faint  that  they  cause  no  noticeable  winds." 

But  the  slight  barometic  depressions  and  cyclonic  motions 
over  a  considerable  area  are  often,  perhaps  generally,  not  ob- 
served, but  a  sudden  change  of  temperature  and  pressure  and 
a  corresponding  sudden  wind-squall  generally  from  some  north- 
westerly direction.  The  sudden  change  of  temperature  is 
usually  10°  to  20°  or  25°  F.,  and  the  corresponding  changes  of 
barometric  pressure  rarely  amount  to  as  much  as  O.I  of  an  inch 


452  THUNDER-S  TO  RMS. 

(2.5  mm.),  and  these  changes  take  place  mostly  in  about  ten- 
minutes.  In  India  the  change  of  temperature  is  said  to  be 
only  10°  to  12°  F.,  while  the  change  of  pressure  is  from  0.8  to 
0.15  of  an  inch,  the  greater  part  of  which  always  occurs  very 
suddenly.  The  corresponding  sudden  increase  of  the  wind 
here  often  amounts  to  from  40  to  60  miles  an  hour. 
In  Italy,  according  to  Ferrari,90 

"Before  the  thunder-storm,  the  pressure  and  the  relative  humidity  fall 
and  the  temperature  rises  in  such  a  manner  that  the  first  two  reach  a 
minimum  and  the  last  a  maximum  at  the  moment  of  commencement  of 
the  thunder-storm;  then  the  pressure  and  the  relative  humidity  rise 
rapidly  and  the  temperature  falls,  and  both  of  the  first  often  reach  a 
maximum  and  the  last  a  minimum  by  the  end  of  the  storm.  The  change 
of  temperature  is  exactly  the  reverse  of  that  of  the  relative  humidity  and 
of  the  pressure.  The  velocity  of  the  wind,  before  the  thunder-storm 
small  or  very  nearly  nothing,  increases  rapidly  with  the  commencement 
of  the  storm,  reaches  its  maximum  at  the  end  or  shortly  after,  and  then 
rapidly  falls  again." 

It  should  be  observed  here  that  the  changes  of  temperature, 
and  the  corresponding  reverse  changes  of  relative  humidity, 
necessarily  take  place  from  the  changes  of  capacity  of  the  air 
for  moisture  with  changes  of  temperature,  and  do  not  indicate 
any  corresponding  changes  in  the  absolute  amount  of  moisture 
in  the  air  before  and  after  the  thunder-storm  sets  in.  Although 
the  relative  humidity  is  greater,  yet  it  is  most  probable  that 
the  absolute  amount  of  vapor  is  less  after  than  before  the  storm. 

299.  On  the  evening  of  June  7,  1885,  barographic  curves 
were  obtained  at  Ann  Arbor  (Michigan)  of  two  thunder-storms 
which  passed  over.  These  are  described  in  the  same  words 
which  had  been  used  to  describe  similar  changes  during  thun- 
der-storms observed  at  Berlin: 

"Before  the  outburst  of  the  thunder-storm,  the  curves  sank  slowly, 
next  rose  steeply  to  a  considerable  height ;  .  .  .  the  curve  then  main- 
tained itself  at  a  level  for  some  time,  throughout  which  the  thunder- 
shower  or  hail  was  wont  to  fall ;  on  the  cessation  of  rain,  the  atmos- 
pheric pressure  sank  steeply.  .  .  ." 

It  is  also  stated  in  the  same  connection  : 

"  Eye  observations  of  the  barometric  height  were  also  taken  during  the 
first  storm  at  Ann  Arbor,  and  immediately  after  the  beginning  of  the 


OBSERVED  PHENOMENA.  453 

rainfall  the  barometer  was  observed  to  rise  0.07  of  an  inch  in  about  ten 
minutes,  then  remained  nearly  stationary  for  about  20  minutes,  when  it 
began  to  sink.  Preceding  this  thunder-storm  (which  came  up  from  the 
west),  the  wind  had  been  blowing  pretty  steadily  from  the  west  for  an 
hour  or  two  at  the  rate  of  12  miles  per  hour;  but  as  the  thunder-storm 
approached,  it  fell  to  a  velocity  of  about  5  miles  and.  coincident  with  the 
rise  of  pressure,  increased  to  a  velocity  of  24  miles  per  hour,  which  it 
maintained  for  about  15  minutes,  then  in  less  than  an  hour  decreased  to 
a  velocity  of  about  3  miles,  having  shifted  in  direction  from  the  west  to 
the  east,  but  soon  rose  again  to  a  velocity  of  6  miles.  The  phenomena 
connected  with  the  second  storm  were  very  similar,  except  that  the  wind 
fell  from  its  highest  velocity  of  about  30  miles  to  an  almost  calm  within 
ten  minutes;  but  soon  rose  again  to  a  velocity  of  nine  miles  from  the  S. 
E.,  which  continued  for  several  hours.  These  changes  of  wind  velocity 
are  in  accordance  with  the  supposition  that  there  was  an  indraught  of  air 
toward  the  cloud  in  front  and  rear  of  the  storms,  but  that  immediately 
under  the  storm  there  was  an  outward  movement  in  every  direction,  the 
different  effects  at  the  earth's  surface  in  front  and  rear  of  the  storm  being 
•due  to  the  movement  of  the  thunder-storm  along  the  earth's  surface."  8a 

300.  According  to  observation,  thunder-storms  often  ap- 
pear in  groups,  all  progressing  eastwardly,  in  parallel  directions, 
some  abreast,  and  others  following  after.  Hence  there  is  often 
a  succession  of  such  storms  at  the  same  place  within  a  short 
period  of  time,  as,  the  same  afternoon.  Thus  on  July  29,  1885, 
five  separate  storms  were  traced  in  the  southern  part  of  New 
Hampshire  and  the  eastern  part  of  Massachusetts.  Of  the 
last  and  most  extensive  of  these  it  is  said  : 

"  It  does  not  seem  to  have  been  a  well-united  storm,  but  consisted  of 
numerous  loosely  connected  parts,  from  which  showers  of  varying 
strength  fell."  81 

On  July  3  there  was  a  group  of  thunder-storms  in  central 
and  southern  Massachusetts  and  central  and  south  New  Hamp- 
shire, of  which  no  less  than  ten  could  be  traced  from  the  obser- 
vations. There  may  have  been  a  hundred  different  centres  of 
action  around  which  rain  and  thunder  occurred  over  progres- 
sive areas,  of  greater  or  less  extent  and  of  various  times  of  du- 
ration, from  which  no  reports  were  received.  In  such  a  thun- 
der-storm area  there  may  be  such  a  blending  of  the  different 
storms  that  there  are  few  places  where  rain  does  not  fall  and 


454  THUNDER-STORMS. 

thunder  is  not  heard,  and  so,  from  reports  received  from  a  lim- 
ited number  of  stations,  it  may  seem  to  be  one  homogeneous 
storm  area.  But  even  the  reports  often  indicate  that  this  is 
not  the  case,  as  is  seen  above  in  the  extract  from  the  report  of 
the  storm  of  July  29,  but  that  it  consists  of  numerous  loosely 
connected  parts.  In  all  such  cases  the  relation  of  each  distinct 
storm  area  to  the  general  storm  area  is  the  same  as  that  of 
heavy  showers  to  the  general  rain  area  on  a  larger  scale,  §  209, 
where  the  atmosphere  over  a  large  area  is  in  the  unstable  state, 
but  in  which  the  conditions  have  not  been  such  as  to  give  rise 
to  a  cyclone.  It  is  simply  one  of  the  numerous  places  where  as- 
cending currents  are  for  some  reason  started  more  than  at 
other  places,  which  give  rise  to  rain  and  generally  thunder,  but 
in  which  the  condition  is  generally  absent  which  gives  rise  to 
rotary  circulation. 

The  general  form  of  the  rain  area  at  any  given  time  in  a 
compact  group  of  simultaneous  storms,  and  even  where  it  may 
be  regarded  as  one  solid  storm,  is  no  doubt  very  different  in 
different  cases,  and  in  the  same  storm  different  at  different 
times.  In  the  case  of  the  storm  in  New  England,  July  21, 
1885,  the  average  form  seems  to  have  been  that  of  the  annexed 
figure,  as  obtained  from  a  composite  portrait  of  the  forms  at 


E 


Fig.  I. 

different  times.81  This  also  seems  to  be  the  form,  according 
to  Dr.  Hinrichs,  of  the  front  convex  part  of  the  storms  and 
squalls  of  Iowa.  \ 


OBSERVED  PHENOMENA.  455 

"  In  northeastern  Iowa  the  storm-front  has  a  tendency  to  bend  up,  so 
as  to  make  the  squall  below  more  nearly  from  the  west.  In  a  like  man- 
ner in  southwestern  Iowa  its  front  bends  westward  and  hence  blows  more 
nearly  from  the  north." 

The  convex  front  part  of  such  storms  generally  seems  to  be 
well  determined  where  the  rain  area  assumes  a  somewhat  regu- 
lar form  of  any  kind  ;  but  even  this  is  often  represented  to  be 
quite  irregular  and  ill-defined. 

According  to  Ferrari,90  as  observed  in  Italy, 

"  Thunder-storm  days  generally  exhibit  two  different  types  of  storms : 
in  the  one  the  thunder-storm  activity  is  divided,  and  in  the  other  one  a 
large  thunder-storm  is  formed,  usually  accompanied  by  others  of  smaller 
extent.  In  the  first  case  small  thunder-showers  are  formed  here  and 
there  which  follow  after  and  encroach  upon  one  another;  such  appear 
almost  exclusively  during  the  midday  and  afternoon  hours,  especially 
between  i  and  4  P.M.  In  the  second  case  a  single  thunder-storm  ex- 
tends over  a  large  area  in  a  certain  interval  of  time,  while  the  smaller 
thunder-storms  which  appear  on  these  days  preserve  their  usual  charac- 
ter almost  exclusively  and  prefer  the  afternoon  hours.  It  is  sure  to  hap- 
pen that  the  more  extended  storm  on  such  a  day  is  composed  of  more 
than  one ;  but  at  all  events,  even  in  this  case,  a  thunder-storm  takes  place 
wfyich  we,  on  account  of  its  character,  call  the  '  principal  storm.'  Such 
a  principal  storm  is  often  the  last  to  occur,  and  that  which  properly  ends 
the  thunder-storm  activity  of  the  period  ;  in  other  cases  it  is,  on  the  other 
hand,  followed  by  smaller  thunder-storms." 

301.  The  antecedent  and  following  observed  phenomena 
are  usually  somewhat  as  follows,  as  deduced  from  a  graphic 
average  by  means  of  a  composite  portrait  in  the  case  of  the 
storm  of  July  9,  1885,  in  New  England  : 

"  An  hour  and  a  half  or  an  hour  before  the  storm,  clouds  are  seen  ris- 
ing on  the  western  horizon,  while  the  winds  are  lightly  southerly,  and 
the  temperature  high  (85° — 95°).  Nearer  the  storm-front,  the  clouds  are 
seen  to  rise  higher,  and  the  temperature  falls  slightly,  but  the  wind  does 
not  change  significantly.  The  first  thunder  is  heard  from  thirty  to  sixty 
minutes,  and  the  clouds  are  recorded  as  reaching  the  zenith  or  passing 
overhead  from  ten  to  thirty  minutes  before  the  rain.  The  sudden 
change  from  gentle  southerly  wind  to  the  northwest  squall  seldom  comes 
more  than  fifteen  minutes  before  the  rain,  and  is  generally  only  five  to 
.seven  minutes  before  it;  with  this  change  the  temperature  falls  rapidly. 
The  squall  seldom  continues  after  the  rain  begins.  The  heaviest  rain  is 


456  THUNDER-STORMS. 

marked  close  to  the  rain-beginning  in  many  cases  ;  in  others  it  falls  from 
seven  to  twenty-five  minutes  later.  The  loudest  thunder  runs  from  ten 
to  thirty  minutes  after  the  rain-front,  and  the  lightning-strokes,  as  far  as 
reported,  fall  with  one  exception  between  thirteen  and  twenty-seven  min- 
utes after  the  rain-front.  Already  at  twenty  to  twenty-five  minutes  after 
the  rain  had  begun,  the  western  horizon  is  seen  lighting  up,  and  soon  the 
clouds  begin  to  break  away  ;  the  rear  edge  is  overhead  in  an  hour  to  an 
hour  and  a  half,  while  the  rain  had  ceased  fifteen  minutes  sooner  on  the 
average,  its  shortest  duration  being  thirty  and  its  longest  ninety  minutes. 
During  the  rain  the  temperature  stood  fifteen  to  twenty-five  degrees 
lower  than  before  the  storm,  and  the  winds  were  light  and  variable  ;  as 
the  storm  passed  over  in  the  afternoon,  an  absolute  rise  of  temperature 
after  its  passage  is  seldom  seen,  and  then  is  faint ;  but  a  relative  rise  is 
clearly  found  in  the  maintenance  of  an  almost  uniform  temperature  past 
those  hours  when  it  ordinarily  decreases  most  rapidly.  Rainbows 
make  their  appearance  between  an  hour  and  an  hour  and  a  half  after 
the  rain-beginning,  and  the  last  thunder  is  heard  from  one  to  two  hours 
after  the  storm  began."  81 

302.  Although  the  rain-area,  as  represented  in  Fig.  I,  may 
have  considerable  width,  yet  the  energy  and  violence  of  the 
storm  is  mostly  around  on  the  front  and  convex  edge ;  in  fact 
it 'seems  from  accounts  that  the  whole  storm  often  assumes  the 
form  of  a  long  extended  and  narrow  band  lying  somewhat 
transverse  to  the  direction  of  general  progressive  motion,  but 
mostly,  at  least  in  New  England,  considerably  inclined,  as  the 
southeasterly  side  of  Fig.  I.  In  Italy,  according  to  Ferrari,90 
from  the  few  cases  in  which  he  could  observe  the  beginning, 

"  the  origin  of  a  thunder-storm  was  a  point.  From  this  it  spread  out, 
not  on  all  sides,  but  only  in  one  direction,  as  is  represented  in  Fig.  5  [here 
the  following  figure  (2)].  I  believe  that  this  may  generally  be  the  way 
in  which  the  thunder-storm  arises.  At  first,  also,  the  form  of  the  thun- 
der-storm is  that  of  the  sector  of  a  circle,  out  of  which  it  gradually 
passes  into  that  of  a  band  of  a  greater  or  less  length." 

On  the  24th  of  June,  1888,  the  writer  observed  the  first 
formation  of  a  thunder-storm  almost  vertically  over  Kansas 
City,  Mo.  A  little  before  II  A.M.  a  circular  dark  cloud  ap- 
peared a  little  to  the  north  and  east  of  his  point  of  observation, 
while  toward  the  west,  and  in  nearly  all  directions,  there  were 
visible  spots  of  clear  sky.  The  first  thunder  was  heard  in  this 


OBSERVED  PHENOMENA.  457 

cloud  nearly  overhead.  It  continued  to  darken  and  to  spread 
at  first  in  all  directions,  and  soon  there  was  an  unusually  heavy 
shower  of  rain,  which  continued  nearly  an  hour.  Before  it 
ended  the  cloud  seemed  to  cover  the  whole  heavens  evenly  in 
all  directions,  and  the  thunder  was  heard  on  all  sides.  The 
upper  clouds  before  and  after  the  shower  had  a  scarcely  percep- 
tible motion  in  a  direction  from  W.S.W.,  and  there  was  very 
little  surface  wind.  During  the  rain  there  was  a  wind  blowing 
out  from  the  place  where  the  cloud  first  formed  toward  the 


W.S.W.  The  breaking  and  thinning  out  of  the  clouds  first 
took  place  in  the  west,  and  the  thunder-cloud,  as  usual,  passed 
slowly  away  in  an  easterly  direction.  The  origin  of  this 
thunder-storm  was  evidently  similar  to  those  observed  by 
Ferrari,  but  whether  it  continued  its  progressive  motion  a  long 
distance  and  expanded  laterally  as  it  went,  as  represented  in 
Fig.  2,  is  not  known. 
In  Bavaria,80 

"When  lines  are  drawn  so  as  to  include  the  whole  district  over  which 
thunder  is  heard  at  a  given  time,  the  area  thus  occupied  is  found  to  be  a 
long,  narrow  band,  at  right  angles  to  the  storm's  path.  Storms  are  fre- 
quently observed  that  stretch  from  the  northern  limits  of  Bavaria  to  the 
Alps,  about  200  miles,  while  their  breadth  (determined  by  audible  thun- 
der) is  at  highest  50  miles,  generally  about  25  miles,  and  often  much 
less.  In  such  cases  the  whole  length  of  the  storm-band  is  not  meas- 
ured." 

Of  such  storms  in  Iowa  it  is  said : 

"  The  storm-front  is  fierce  in  its  power  along  a  considerable  distance ; 
20  to  50  miles  and  more  in  its  front  along  the  earth  are  struck  simulta- 
neously. As  the  great  storm -front  sweeps  on,  it  generally  diminishes  in 
fury,  but  at  times  it  can  be  traced  for  350  miles  from  the  northwest  to 
the  southeast  of  our  State." 


458 


THUNDER-STORMS. 


In  Switzerland  at  least  there  seem  to  be  thunder-storms, 
which  do  not  have  the  usual  easterly  progressive  motion,  but 
sometimes  the  contrary.  It  is  said  : 

"  The  storm  occupies  at  first  a  small  area,  and  then  expands  in  nearly 
all  directions,  its  front  lines  being  sharply  bent,  almost  closed,  curves." 

But  the  front  lines  generally  seem  to  be  similar  to  those 
represented  in  the  preceding  figure,  and  the  great  convexity 
on  the  one  side  undoubtedly  arises  from  the  tendency  to 
spread  faster  in  this  direction  than  in  any  other,  while  in  Italy 
and  most  other  places  the  directions  of  spreading  are  confined 
within  a  small  range  of  easterly  directions,  and  there  is  a  dying 
out  of  the  storm  in  other  directions. 

The  accompanying  plate  is  a  sketch   of  a  thunder-storm 


THUNDER-STORM   OBSERVED   OFF   THE   COAST   OF   MAINE,    JULY,    1883. 

taken  by   Mr.  Morey    off  the    coast   of  Maine,  in    July,  1883. 
The  following  is  his  account  of  it: 

"  The  point  of  observation  was  about  two  miles  out  at  sea. 

"The  storm  occurred  during  a  clear  sultry  afternoon,  and  moved 
from  a  southwesterly  to  a  northeasterly  direction,  accompanied  by  a 
great  display  of  electricity  and  a  large  amount  of  rain. 

"The  cumuli  on  the  top  of  the  cloud-bank  were  of  almost  snowy 


THE    THEORY.  459 

whiteness,  growing  rapidly  darker  to  the  almost  black  strata  forming 
the  base. 

"  Previous  to  the  disturbance  the  distant  sky  was  perfectly  clear  except 
in  the  southwest,  where  a  few  dun-colored  cumuli  seemed  to  rest  on  the 
land.  The  wind  was  extremely  light.  These  conditions  remained  after 
the  passage  of  the  storm,  with  the  exception  that  the  cumuli  in  the  south- 
west had  disappeared  and  the  wind  blew  fresher  from  the  northwest. 
Duration  of  storm,  30  minutes." 


THE  THEORY. 

303.  The  fundamental  conditions  of  thunder-storms,  as  of 
cyclones  and  tornadoes,  are  the  state  of  unstable  equilibrium, 
at  least  for  saturated  if  not  for  dry  air,  and  a  high  relative  hu- 
midity. The  less  the  latter,  the  more  nearly  must  the  state 
of  the  air  approximate  to  that  of  the  unstable  state  of  dry 
air.  From  these  conditions  rapidly  ascending  currents  and  a 
vertical  circulation  arise,  just  as  in  the  case  of  cyclones  and 
tornadoes,  and  a  condensation  of  aqueous  vapor  and  a  fall  of 
rain  or  hail  takes  place  in  the  ascending  current,  accompanied 
generally  in  summer  by  electrical  phenomena.  In  what  are 
usually  called  thunder-storms,  the  conditions  are  nearly  or 
quite  absent  which  give  rise  to  a  gyratory  circulation  over  a 
large  area,  such  as  takes  place  in  the  case  of  cyclones,  and  usu- 
ally the  conditions  are  wanting  which  give  rise  to  small  local 
and  violent  tornadic  gyrations,  though,  as  we  have  seen,  §  297, 
most  tornadoes  are  thunder-storms.  Since  secondary  cyclones, 
tornadoes,  and  thunder-storms  are  dependent  upon  great  hu- 
midity and  the  unstable  state  of  the  atmosphere,  it  is  reasona- 
ble to  suppose  that  they  must  be  found  to  exist  together  often 
in  the  same  region  having  these  conditions,  and  that  there  is  a 
running  together  and  a  blending  of  the  several  forms  of  the 
storms  without  any  distinct  dividing  line.  Hence  we  find  that 
there  are  thunder-storms  with  more  or  less  cyclonic  motions 
and  local  depressions,  that  they  occur  in  regions  where  there 
are  secondary  cyclones,  and  that  tornadoes  are  frequently  ob- 
served in  connection  with  thunder-storms.  In  order  to  the 
latter,  it  is  merely  necessary  that,  in  addition  to  the  general 


460 


THUNDER-  S  TO  RMS. 


conditions,  there  shall  also  be  the  condition,  where  the  unsta- 
ble air  at  any  point  bursts  up  through  the  strata  above,  which 
gives  rise  to  the  violent  tornadic  gyrations  also. 

We  have  seen  that  the  thunder-storms  seem  often  to  arise 
at  some  given  point  and  to  enlarge  and  extend  mostly  in  some 
easterly  direction,  but  when  the  air  is  in  the  unstable  state  it 
is  liable  to  burst  up  and  to  give  rise  almost  simultaneously  to 
many  ascending  currents  and  centres  of  local  thunder-showers, 
which  spread  and  eventually  somewhat  blend  together  so  as  to 
form  apparently  only  one  thunder-storm,  while  in  reality  it  is 
composed  of  a  number  of  loosely  connected  parts,  as  in  the 
-case  of  the  thunder-storms  of  July  3,  referred  to  in  §  300. 

Where  the  ascending  current  of  one  of  these  points  of 
eruption  is  unusually  strong  and  reaches  to  great  altitudes, 
though  there  may  not  be  much  violent  tornadic  action,  it  gives 
rise  to  hail  in  the  interior  of  the  thunder-storm.  Hence  Ferrari 
states90  "  that  in  the  region  passed  over  by  thunder-storms  the 
hail  extended  in  small  strips  in  the  direction  of  motion." 

304.  Let  us  consider  first  the  case  of  a  simple  thunder- 


a, 


c 

Fig.  3. 


fforey.' 


-storm  under  conditions  which  are  homogeneous  on  all  sides, 
and  in  which  the  air  has  no  progressive  motion  in  any  direc- 


THE    THEORY. 


461 


tion.  If  the  air  is  in  the  unstable  state,  and  over  a  given  cir- 
cular area  of  diameter  ab,  Fig.  3,  is  a  little  warmer  and  lighter 
than  that  of  the  surrounding  parts,  or  for  any  reason  receives 
an  upward  motion,  there  is  set  up,  in  the  manner  heretofore 
explained,  a  vertical  circulation  with  an  ascending  current  in 
the  interior  over  and  around  the  centre  c,  and  an  incoming  cur- 
rent from  all  sides  in  the  lower  part  of  the  air  to  supply  the 
ascending  current,  as  indicated  by  the  arrows  in  the  figure ; 
while  above,  the  current  is  outward  in  all  directions,  and  there 
is  a  slow  descent  or  settling  down  of  the  air  on  all  sides.  In 
the  interior  ascending  current  the  height  of  incipient  condensa- 


fe. 


Vvw  *ivv*>M 


'  ,/  \  v    y  '      v     /MO 

^x     t    v  ^     '    ^  ~    y    »   w 


Fig.  4. 

tion  and  of  the  base  of  the  cloud  depends  upon  the  depression  of 
the  dew-point  of  the  air,  and  the  aqueous  vapor  above  that 
height  is  condensed,  falls  as  rain,  and  cools  the  air  through 
which  it  falls,  as  already  explained,  until  its  temperature  is 
lower  than  that  of  the  surrounding  air.  This  central  cooled 
air,  being  now  heavier  than  the  surrounding  air,  both  on  ac- 
count of  its  greater  density  and  the  amount  of  falling  rain 
pressing  on  it,  now  gradually  settles  down  and  causes  an  out- 
ward current  in  all  directions  from  the  centre  c,  Fig.  4.  At  cr, 
Fig.  4,  there  is  a  maximum  of  pressure  which  decreases  on  all 


462  THUNDER-  S  TO  RMS. 

sides  toward  c,  but  at  some  point  between  c'  and  c,  but  much 
nearer  to  c  after  the  ring  has  expanded  considerably,  there  is  a 
very  steep  part  in  both  the  temperature  and  pressure  gradient, 
exactly  under  the  vertical  between  the  warmer  ascending  cur- 
rent on  the  one  side,  and  the  colder  descending  current  on  the 
other,  where  most  of  the  change  of  pressure  takes  place  in 
about  ten  minutes  generally,  and  where  the  squall  exists,  which 
encounters  the  inflowing  current  from  all  sides,  and  both. are 
gradually  retarded  and  deflected  upward,  and  there  is  now  a 
ring  of  ascending  air,  the  middle  of  which  is  at  the  distance  of 
•c'  from  the  centre.  This  ring  of  ascending  air  in  turn  becomes 
cooled  down  and  changed  to  a  descending  current  in  precisely 
the  same  way  as  the  first  central  ascending  current  was,  and 
another  ring  of  ascending  air  with  its  middle  at  a  greater  dis- 
tance from  the  centre  is  developed,  and  so  on ;  and  this  is  con- 
tinued as  long  as  the  air  is  in  the  unstable  state.  As  the  air 
on  the  interior  side  of  the  ring  is  gradually  cooled  down  and 
changed  to  a  descending  current  and  flows  under  it,  more  of 
the  air  on  the  other  side  is  thrown  up  into  an  ascending  cur- 
rent, and  the  ring  progresses  and  enlarges  somewhat  as  a  wave 
of  water  flowing  out  from  a  central  point. 

In  Switzerland,  according  to  observation,  §  302,  the  condi- 
tions of  this  case  are  sometimes  nearly  satisfied,  since  the 
storms  expand  in  nearly  all  directions  and  their  front  lines  are 
almost  closed  lines.  In  Switzerland,  in  summer,  the  velocity 
of  the  general  easterly  progression  of  the  air  is  small  at  all 
altitudes,  and  on  the  north  side  of  a  cyclone  there  may  be  no 
such  motion;  so  that  it  may  happen  that  the  conditions  of  this 
case  may  be  nearly  or  quite  satisfied  here  in  some  cases. 

305.  In  what  immediately  precedes,  the  air  is  supposed  to 
be  at  rest  on  the  earth's  surface  and  homogeneous,  or  at  least 
symmetrical,  on  all  sides  of  the  centre,  and  the  area  is  so  small 
at  first  that  it  is  not  thrown  into  any  sensible  gyration  around 
the  centre.  There  is  consequently  no  reason  why  it  should 
progress  as  a  whole  in  any  one  direction  rather  than  another, 
and  whatever  changes  occur  must  take  place  equally  and  sym- 
metrically in  all  directions.  But  if  one  side,  as  the  south  side, 


THE    THEORY.  463 

is  warmer  and  moister  than  the  other,  then  the  supply  of 
•energy  which  keeps  up  the  vertical  circulation  is  strongest  on 
that  side ;  and  although  the  tendency  is  still  to  spread  in  all 
directions,  yet  it  does  so  mostly  on  this  side. 

Again,  if  we  suppose  the  whole  system  to  be  stationary, 
but  that  there  is  a  current  of  air  in  the  lower  stratum  next  the 
earth's  surface  passing  in  any  direction  under  it,  as  a  southerly 
or  easterly  surface  wind,  this  brings  the  warm  moist  surface  air 
in  below  on  the  windward  side,  and  carries  the  comparatively 
-cool  and  dry  air  of  the  interior  out  to  the  other  side,  and  there  is, 
consequently,  an  unequal  distribution  of  energy  on  the  two  sides, 
and  a  tendency  in  the  ring  to  spread,  and  the  whole  system  to 
move  mostly,  if  not  entirely,  in  the  direction  from  which  the 
wind  and  the  energy  come.  We  have  a  similar  case  if  there 
is  a  wind  in  a  great  conflagration,  as  in  a  city,  where  the  burn- 
ing material  is  distributed  equally  and  symmetrically  in  all 
directions.  The  fire  extends  mostly,  if  not  entirely,  in  the  di- 
rection from  which  the  wind  comes,  because  on  that  side  is  the 
supply  of  oxygen  mostly  to  sustain  the  combustion,  while  on 
the  other  side  there  is  air  which  has  passed  through  the  flame 
and  has  had  its  oxygen  mostly  burnt  out. 

We  have  a  case  similar  to  the  preceding  relatively,  where 
the  whole  atmosphere  has  a  regular  progressive  motion,  say 
toward  the  east,  but  the  part  nearest  the  earth's  surface  is  re- 
tarded by  frictional  resistance  of  that  surface. 

The  more  slowly  moving  stratum  next  the  earth  is  rela- 
tively a  wind  blowing  under  the  storm  from  the  direction  in 
which  the  storm,  drifting  in  the  strata  above,  is  progressing, 
and  consequently  the  effect  is  the  same,  and  the  tendency  is 
for  the  storm  not  only  to  spread  in  that  direction  relatively  to 
the  air  in  which  it  exists,  but  even  to  subside  and  die  out  in 
the  rear,  and  so  to  not  progress  in  that  direction.  The  storm 
then  assumes  the  form  of  Fig.  I.  It  not  only  drifts  in  an  east- 
erly direction  with  the  general  motions  of  the  air,  but  it  pro- 
gresses also  relatively  to  the  air,  mostly  in  this  direction,  and 
it  also  spreads  a  little  toward  the  south  on  account  of  the  air 
on  that  side  being  warmer  and  moister,  and  this  is  especially 


464  THUNDER  STORMS. 

the  case  where  there  is  a  southerly  wind,  as  there  usually  is  in 
thunder-storms ;  but  it  progresses  or  spreads  but  little  if  any 
toward  the  north.  For  this  reason  we  have  the  unsymmetrical 
form  of  the  storm  with  reference  to  the  apex  and  axis  of  pro- 
gression, as  represented  in  Fig.  I.  The  progress  is  mostly 
toward  the  east,  but  also  toward  the  south,  and  there  is  a  grad- 
ual dying  out  of  the  storm  in  the  rear  and  on  the  north  side, 
leaving  a  much  longer  wing  or  branch  extending  back  on  the 
south  than  on  the  north  side,  which  is  supported  and  kept  up 
by  the  greater  energy  on  that  side  arising  from  warmer  and 
moister  air,  if  not  also  from  surface  southerly  winds,  which 
blow  somewhat  under  the  strata  above,  moving  more  in  an 
easterly  direction. 

306.  Whatever  the  form  which  the  thunder-storm  may  as- 
sume, whether  that  of  §  304,  in  which  there  is  an  enlargement 
and  a  spreading  in  nearly  all  directions  without  'much  progres- 
sive motion  in  any  direction,  or  that  of  §  305,  in  which  there  is 
an  easterly  progressive  motion,  and  the  rain  and  the  storm 
areas  are  of  the  form  of  Fig.  I,  or  even  more  nearly  a  mere 
narrow  convex  band  progressing  as  a  wave  and  increasing  in 
length  as  it  goes,  as  represented  in  Fig.  2,  there  is  a  steep  but 
short  pressure  gradient  around  the  front  border  of  the  rain  area 
as  it  progresses,  which  often  gives  rise  to  a  sudden  and  violent 
squall  where  it  passes  over  any  place,  but  usually  only  to  a 
gentle  wind  blowing  out  from  under  the  thunder-cloud.  This 
pressure  gradient  has  been  attributed  to  the  difference  of  tem- 
perature within  a  short  horizontal  distance  of  the  point  c'r 
Fig.  4,  between  the  contiguous  portions  of  air  in  which  rain  has 
not  yet  commenced  to  fall  and  that  in  which  rain  is  falling. 
The  rain  having  been  produced  by  the  condensation  of  vapor,, 
at  least  in  part,  up  in  the  high  and  cold  strata,  and  then  carried 
by  the  ascending  current  still  higher,  much  of  it  is  cooled  down 
to  a  low  temperature,  and,  it  may  be,  even  frozen  into  hail.  In 
falling  slowly  through  the  air  it  cools  it  to  a  temperature  con- 
siderably lower  than  that  of  the  contiguous  air  through  which 
rain  has  not  yet  commenced  to  fall,  and  hence  the  great  differ- 
ence of  temperature  and  of  pressure  within  a  short  distance. 


THE    THEORY.  46$ 

The  cooling  of  the  air  is  also  increased  by  the  evaporation  of 
the  rain  in  falling  through  the  lower  unsaturated  air,  and  also 
by  the  melting  of  the  hail  in  the  case  of  hail-fall.  These  seem 
to  have  been  the  causes  assigned  by  Dr.  Koppen  in  his  explana- 
tion of  the  phenomena  in  the  thunder-storm  of  August  9,  1881, 
which  passed  over  Germany,  so  far  as  the  writer  can  learn  in  a 
second-hand  way  from  extracts  from,  and  references  to,  his 
paper  on  that  subject,  and  they  are,  no  doubt,  the  true  causes. 

307.  A  difference  of  i°  C.  in  the  temperature  of  two  con- 
tiguous portions  of  the  atmosphere  extending  to  the  top  would 
give  a  difference  of  barometric  pressure  of  2.8  mm.  (o.n  of  an 
inch),  which  may  be  considered  as  a  somewhat  extreme  differ- 
ence, as  observed  in  thunder-storm  squalls,  though  of  course  it 
is  undoubtedly  much  more  in  very  destructive  squalls,  in  which 
observations  cannot  be  made.  This,  by  the  formula  of  §  235, 
gives  at  the  earth's  surface,  where  we  have  P  =  P0  and  T,  say, 
equal  to  T9  +  30°  =  303°,  s  =  25  m.  p.  s.,  or  about  56  miles 
per  hour,  for  the  velocity  of  the  wind  in  the  squall  arising  from 
this  difference  of  pressure  in  case  of  no  friction.  Making  con- 
siderable allowance  for  this,  which  is  always  necessary  in  such 
cases,  we  still  have  a  destructive  squall,  and  one  which  usually 
corresponds  to  a  difference  of  pressure  of  that  order.  In  the 
observation  of  Mr.  Clayton,  §  299,  the  difference  of  pressure  of 
0.07  of  an  inch  (1.78  mm.)  by  the  same  formula  gives  s  =  19 
m.  p.  s.,  or  nearly  43  miles  an  hour.  Making  a  very  liberal  al- 
lowance for  friction,  we  still  have  the  greatest  observed  velocity 
of  24  miles  an  hour,  as  obtained  in  his  observations. 

We  see  that  a  difference  of  temperature  of  i°  C.  extending 
to  the  top  of  the  atmosphere  would  give  rise  to  a  difference  of 
pressure  from  which  would  result  a  destructive  squall.  But 
thunder-storms  and  differences  of  temperature  in  contiguous 
portions  of  the  atmosphere  do  not  reach  to  the  top,  perhaps 
often  not  very  far  up.  But  say  the  observed  difference  at 
the  earth's  surface  is  6°  C.,  and  that  it  gradually  and  uniformly 
diminishes  with  increase  of  altitude  and  vanishes  at  the  alti- 
tude which  leaves  one  third  of  the  atmosphere  below  it.  The 
effect  upon  the  difference  of  pressure  upon  this  suppositioa 


466  THUNDER-STORMS. 

would  be  exactly  equal  to  that  of  a  difference  of  i°  C.,  extend- 
ing up  to  the  top.  But  the  observed  difference  of  temperature 
in  the  air  at  the  earth's  surface  before  and  after  the  shower  is 
often  more  than  6°  C.,  and  so  it  is  reasonable  to  suppose  that 
the  difference  so  extends  up  to  the  strata  above  as  to  give  the 
usual  observed  corresponding  difference  of  pressure. 

308.  There  is  still  another  cause  besides  the  lowering  of 
the  temperature  of  the  air  which  may  very  sensibly  increase 
the  air  pressure  in  the  region  of  falling  rain,  and  that  is  the 
pressure  of  the  rain  contained  in  the  air.     This,  in  falling,  soon 
acquires  a  maximum  velocity,  after  which  the  air  pressure  is 
increased  by  the  full  statical  pressure  of  the  rain,  since  the 
whole  force  of  gravity  then  upon  the  rain  is  exerted  by  means 
of  friction  upon  the  atmosphere.     We  cannot  have  generally 
much  idea  of  the  amount  of  rain  and  hail  which  may  be  con- 
tained in  the  air  at  any  time,  but  we  know  from  the  amount 
which  often   falls  suddenly  in  cloud-bursts  that    it   is    some- 
times very  great.     If  there  were  at  any  one  time  rain  and  hail 
falling  with  uniform  velocity  equivalent  to  a  rainfall  of  13.6 
mm.  in  depth,  it  would  increase  the  barometric  pressure  I  mm., 
and  from  this  alone,  by  the  formula  of  §  235,  would  arise  a 
squall  with  a  velocity  of  about    15   m.  p.   s.,  or  34  miles  per 
hour,  making  no  allowance  for  friction. 

As  the  falling  rain,  either  from  its  cooling  effect  upon  the 
air  or  the  direct  effect  of  its  own  pressure,  causes  a  pressure 
gradient,  and  the  maximum  velocity  of  the  squall  is  at  the  foot 
of  the  gradient,  where  the  pressure  is  the  least,  the  squall 
wind  is  felt  a  little  before  the  arrival  of  the  rain,  since  the  mo- 
mentum which  the  air  has  at  the  foot  of  the  gradient  carries  it 
to  some  distance  beyond  before  it  is  counteracted  and  the  cur- 
rent deflected  upward.  Hence  the  beginning  of  the  squall  and 
the  sudden  change  of  the  wind  from  a  southerly  to  a  north- 
westerly direction  occurs  in  New  England  generally  from  five 
to  seven  minutes,  sometimes  considerably  more,  before  the 
commencement  of  the  rainfall  (§  301),  and  on  land  in  dry  and 
dusty  weather  it  usually  raises  a  great  cloud  of  dust. 

309.  In  the  rear  of  the  storm  there  is  a  pressure  gradient, 


ItELA  TION  BE  TWEEN  THUNDER-STORMS  AND  CYCLONES.  467 

but  it  is  more  gradual  without  any  part  which  is  abruptly 
steep,  and  there  is  consequently  a  flowing  out  of  the  air  behind 
the  storm,  relatively  to  the  storm  itself,  but  no  sudden  squall 
observed,  and  a  wind  in  New  England  thunder-storms  is  some- 
times observed  to  blow  out  from  beneath  in  the  rear. 

When  the  whole  atmosphere  has  a  progressive  motion 
somewhat  in  the  direction  in  which  the  squall  blows  in  front, 
the  velocity  of  the  squall  as  observed  on  the  earth  is  the  sum 
of  the  velocity  of  progressive  motion  of  the  air  and  of  the  rela- 
tive velocity  with  which  the  wind  blows  out  from  under  the 
.storm,  and  hence  the  observed  wind  for  this  reason  alone 
would  be  much  stronger  in  front  than  in  the  rear.  As  there 
is  a  gradual  drawing  in  of  the  air  from  all  sides  toward  the 
storm,  or  at  least  toward  the  area  of  ascending  air  whatever  the 
form  of  this  area,  the  air  blowing  out  from  under  the  storm  en- 
counters this  and  brings  it  to  rest  relatively  to  the  storm  at  a 
greater  or  less  distance,  and  at  a  still  greater  distance  relatively 
to  the  earth,  when  the  air  has  a  progressive  motion,  and  hence 
sometimes  a  little  before  the  storm  arrives  a  calm  is  observed. 
Sometimes  the  indrawing  current  is  merely  sufficient  to  reduce 
the  progressive  velocity  a  little,  as  in  the  case  of  the  observa- 
tions at  Ann  Arbor,  Michigan,  where  the  velocity  of  the  west 
wind  was  merely  reduced  from  12  to  5  miles  per  hour  and 
there  was  no  perfect  calm  (§  213).  In  this  case  there  was  a 
blowing  out  behind,  or  a  reversal  of  direction,  with  a  very 
small  velocity. 

RELATION  BETWEEN  THUNDER-STORMS  AND  CYCLONES. 

310.  We  have  seen  that  the  origination  of  thunder-storms 
requires  an  unstable  state  of  the  atmosphere.  If,  therefore, 
this  state  is  induced  more  readily  in  some  parts  of  the  cyclonic 
area  than  in  others,  then  there  must  be  a  preponderance  of 
thunder-storms  in  the  former  over  those  of  the  latter.  But  the 
unstable  state  requires  a  vertical  gradient  of  rapidly  decreasing 
temperature  with  increase  of  altitude,  and  this  is  brought  about 
by  the  passage  of  warm  southerly  currents  in  the  lower  strata 


468  THUNDER-STORMS. 

of  the  atmosphere  under  colder  northerly  currents  above,  either 
absolutely  or  merely  relatively.  By  referring  to  Fig.  I,  §  178,. 
it  is  seen  that  this  occurs  in  a  cyclone  in  about  the  E.  S.  E. 
octant,  and  in  some  measure  in  the  adjacent  octants  on  each 
side  of  this  octant,  in  which  large  north  and  south  components 
of  the  winds  pass,  the  latter  below  under  the  former  above. 
By  referring  to  the  opposite  side  of  the  figure  it  is  seen  that 
just  the  reverse  of  this  takes  place  there,  and  that  in  the  W. 
N.  W.  octant  the  cold  northerly  winds  below  pass  under  the 
southerly  winds  above,  and  that  this  is  the  case  with  regard  to 
large  components  of  these  winds  in  the  adjacent  octants  on 
each  side.  The  tendency,  then,  of  the  cyclonic  circulation 
above  and  below  is  to  produce  an  unstable  state  in  the  E.  S.  E. 
octant,  and  also  in  some  measure  in  the  adjoining  octants,  but 
just  the  reverse  in  the  opposite  octants.  Of  course  the  unsta- 
ble state  may  be  brought  about  anywhere  without  any  cyclonic 
influence,  but  this  influence  favors  it  in  the  E.  S.  E.  and  adja- 
cent octants,  and  works  against  it  in  the  opposite  ones. 

But  there  is  also  another  consideration  in  this  connection. 
Thunder-storms  occur  most  frequently  in  the  warmer  and  mois- 
ter  atmosphere  of  the  lower  latitudes  than  in  the  cooler  and 
drier  air  of  higher  latitudes.  Without,  therefore,  any  of  the 
cyclonic  influence  just  referred  to,  there  would  be  a  maximum 
of  thunder-storm  occurrences  in  the  southern  part  of  a  given 
circular  area  of  considerable  extent,  and  a  minimum  in  the 
northern.  The  resultant  maximum  and  minimum,  therefore, 
of  the  two,  the  maxima  in  the  E.  S.  E.  and  the  S,  and  the 
minima  in  the  opposite  directions  from  the  centre,  would  fall 
somewhere  between,  and  most  likely  nearest  to  those  arising 
from  the  cyclonic  influence,  and  so  the  maximum  of  the  re- 
sultant would  fall  in  the  S.  E.  octant,  and  the  minimum  in  the 
opposite  or  N.  W.  octant. 

Again  it  is  seen  from  a  reference  to  the  same  figure  (§  178), 
that  in  the  interior  of  the  cyclone  the  motion  of  the  air  below 
and  above  is  somewhat  in  the  same  direction,  except  that  it 
inclines  in  toward  the  centre  a  little,  below,  and  out  above,  and 
so  there  is  little  or  no  passing,  relatively,  of  warmer,  southerly^ 


RELA  TION  BETWEEN  THUNDER-STORMS  AND  CYCLONES.  469 

wind  below  under  cooler,  northerly  winds  above,  or  the  reverse, 
in  any  octant  of  the  cyclone,  and  so  the  cyclonic  influence 
which  tends  to  produce  the  unstable  state  or  the  reverse  in 
certain  octants,  is  not  found  in  the  whole  interior  of  the  cy- 
clone. Besides  there  is  little  tendency  in  this  central  region, 
on  account  of  its  smallness,  and  so  the  little  difference  in  lati- 
tude between  the  northern  and  southern  sides,  toward  a  maxi- 
mum frequency  of  occurrence  on  the  south  sides,  or  the  reverse 
on  the  other. 

In  the  outer  part  also  of  the  cyclone,  beyond  the  isobar  of 
about  760  mm.,  the  currents  below  are  feeble,  being  under  the 
region  of  high  pressure,  and  at  and  near  the  middle  of  the  cir- 
cular calm-belt  of  this  high  pressure,  and  the  currents  above 
toward  the  outer  border  of  the  cyclone  cannot  be  supposed  to 
be  very  strong ;  so  the  cyclonic  influence  in  this  whole  outer 
part  in  inducing  an  unstable  state  in  any  octant,  or  the  stable 
state  in  the  opposite,  is  very  small.  Besides  this  is  a  dry 
region,  and  for  this  reason,  also,  thunder-storms  should  rarely 
occur. 

311.  From  what  precedes,  therefore,  thunder-storm  fre- 
quency should  be  confined,  not  only  to  the  S.  E.  octant 
mostly,  but  also,  in  average  cyclones,  within  the  isobars  of 
about  750  and  760  mm.  Let  us  now  compare  these  theoreti- 
cal deductions  with  results  of  observations.  The  latter,  for 
Russia,  are  contained  in  the  following  tables  in  percentages  for 
the  whole  year,  given  by  Klossovsky 80  from  very  numerous  ob- 
servations : 


Octant  

N. 
2-3 

N.E. 
12.6 
9.4 

E. 
8.4 

6.2 

S.E. 
41.4 
46.9 

S. 
9-5 
15-6 

s.w. 
19-3 

15.6 

W. 

1.4 
2.1 

N.W. 
5-1 
4.2 

Thunder-storms  
Hail-storms         .... 

Pressure  in  millimeters  

,.{735 
1740 

740 

745 
0-3 

4.6 

745 
75° 

5-8 

750 

755 

37-5 
<K.S 

755 
760 

48.3 
48.0 

760 
765 

7-9 

II.  2 

765 
770 
O.I 

Hail-storms.  . 

.  0.6 

It  is  seen  from  the  first  of  these  tables  that  by  far  the 
greatest  relative  frequency  of  thunder-storms  is  in  the  S.E. 
octant,  though  there  appears  to  be,  for  some  reason,  a  slight 


470  THUNDER-STORMS. 

secondary  maximum  in  the  S.W.  octant.  And!  according  to» 
the  second  table,  nearly  all  occur  at  the  distance  from  the 
centre  at  which  the  barometric  pressure  ranges  from  750  to 
760  mm.  These  results  accord  with  those  deduced  by  Fron 
from  the  observations  of  thunder-storms  in  France,  who  found 
that  they  occur  in  the  "  dangerous"  half  of  the  depression 
between  the  centre  and  border.  As  the  storms  move  mostly 
from  S.W.  to  N.E.  they  consequently  occur  mostly  in  the  S.E.. 
octant. 

Professor  Hazen83  of  the  Signal  Service,  from  the  study  of 
the  thunder-storms  which  occurred  in  May,  1884,  in  the  United: 
States,  likewise  found  that  thunder-storms  generally  accompany- 
an  area  of  low  pressure,  and  are  found  in  the  S.E.  quadrant  at 
a  distance  of  400  to  500  miles  from  the  centre. 

It  is  seen  that  hail-storms  and  thunder-storms  have  about 
the  same  relative  percentages  in  the  different  octants  and 
average  pressures  or  distances  from  the  centres  of  the  cyclones,, 
and  hence  their  relations  to  the  cyclone  centre  are  the  same. 
The  same  is  true  with  regard  to  tornadoes  generally  and 
thunder-storms.  This  is  what  we  would  expect  from  theo- 
retical considerations,  since  all  depend  upon  the  same  general; 
conditions  of  humidity  and  instability  of  the  atmosphere,  and 
tornadoes,  including  hail-storms,  are  usually  found  in  the. 
thunder-storm  region,  and  simply  require  the  additional  local 
condition  which  gives  rise  to  tornadic  gyrations  and,  in  the 
case  of  hail-storms,  to  ascending  currents  which  extend  to- 
high  altitudes. 

ANNUAL  AND  DIURNAL  INEQUALITIES. 

312.  As  thunder-storms  depend  upon  the  unstable  state,, 
and  this  is  brought  about  mainly  by  the  heating  up  of  the 
earth's. surface  and  lower  strata  of  the  atmosphere,  the  condi- 
tions which  give  rise  to  thunder-storms  occur  mostly  during: 
the  warmest  season  of  the  year  and  the  warmest  part  of  the 
day.  Hence  thunder-storms  are  experienced  mostly  in  summer 
and  in  the  afternoon  of  the  day.  And  where  thunder-storms 


ANNUAL  AND  DIURNAL  INEQUALITIES. 

and  line  squalls  progress  over  the  country  in  connection  with 
cyclones  they  have  been  known  to  cease  at  night  and  com- 
mence again  the  next  day. 

On  the  ocean,  however,  the  reverse  of  this  in  some  measure 
takes  place,  and  there  seems  to  be  a  slight  maximum  during 
the  winter  and  the  night. 

According  to  Buchan,84  of  the  23  thunder-storms  which 
occurred  at  Stykkisholm  in  14  years,  only  one  occurred  in  any 
of  the  six  warm  months  of  the  year  from  April  to  September. 
They  occur  also  mostly  during  the  night.  These  storms  are 
short-lived,  being  in  almost  every  case  restricted  to  one,  or  at 
most  only  a  few  flashes  of  lightning  and  claps  of  thunder. 
Taking  also  the  northwest  stations  of  Scotland  alone,  adjacent 
to  the  ocean,  the  thunder-storm  frequency  is  twice  as  great 
during  the  hours  immediately  after  midnight  as  during  the 
hours  from  noon  to  4  P.M.,  and  the  storms  occur  here  also 
mostly  in  the  winter.  On  the  east  coast  the  reverse  takes 
place,  the  diurnal  maximum  being  in  the  warmer  hours  of  the 
afternoon,  and  very  few  storms  occur  during  the  winter. 

Along  the  coast  of  Norway  also,  according  to  Mohn,  there 
seems  to  be  a  slight  tendency  to  a  winter  maximum,  not  only 
in  storm  frequency,  but  likewise  in  intensity,  and  according  to 
Scott,  Valentia,  Ireland,  has  a  strong  winter  maximum  of 
thunder-storm  frequency. 

The  reason  of  contrast  between  ocean  and  land  in  the  times 
of  the  diurnal  and  annual  maxima  of  thunder-storm  frequency 
is  that  the  unstable  state  of  the  atmosphere  upon  which  these 
storms  depend  is  most  readily  induced  on  the  former  during 
the  colder  part  of  the  day  and  the  year,  and  the  reverse  on 
land.  On  the  latter  the  diurnal  and  annual  changes  are  great 
on  and  near  the  earth's  surface,  in  comparison  with  what  they 
are  in  the  upper  part  of  the  atmosphere  ;  while  on  the  ocean 
the  reverse  is  the  case,  the  diurnal  and  annual  changes  being 
very  small  below  in  comparison  with  what  they  are  above, 
where  they  are  somewhat  the  same  as  over  the  continents. 
The  average  state  of  the  atmosphere,  therefore,  on  the  ocean 
is  more  nearly  that  of  the  unstable  state  in  the  winter  and 


472  THUNDER-STORMS. 

during  the  coldest  part  of  the  night  than  at  other  times,  while 
,the  reverse  is  the  case  on  the  land.  The  unstable  state  is, 
therefore,  more  readily  brought  about  on  the  ocean  at  these 
times,  and  hence  there  is  the  greatest  frequency  of  thunder- 
storms at  night  and  during  the  winter.  For  well-known  reasons 
it  is  just  the  reverse  of  this  on  land. 

But  we  have  seen  (§  122)  that  the  western  sides  of  the  con- 
tinents in  middle  and  higher  latitudes  partake  of  an  oceanic, 
rather  than  of  a  continental,  climate ;  and  hence  nocturnal  and 
winter  maxima  occur,  not  only  on  the  ocean,  but  likewise  on 
the  western  sides  of  the  continents  to  some  distance  into  the 
interior. 

The  average  state  of  the  atmosphere  on  land  is  nearer  to 
the  unstable  state  during  the  summer  and  the  warmer  part  of 
the  day  than  it  is  on  the  ocean  during  the  winter  and  the 
colder  part  of  the  day ;  and  hence  upon  the  whole  there  must 
be  more  thunder-storms  upon  land  than  upon  the  ocean,  and 
to  some  extent  on  the  eastern  than  on  the  western  sides  of  the 
continents  in  the  middle  and  the  higher  latitudes.  For  this 
reason  thunder-storms  and  all  small  local  storms  depending 
upon  the  unstable  state  of  the  atmosphere  are  of  greater  fre- 
quency, on  the  average  of  the  year,  on  land  than  on  the  ocean  ; 
and  this  is  especially  the  case  in  the  interiors  of  the  continents, 
while  small  parts  of  the  western  sides,  for  reasons  already  given, 
are  exceptions. 


APPENDIX. 


CONTAINING  THE  TABLES  AND  A  LIST  OF  THE 

BOOKS   AND    PAPERS   REFERRED   TO 

IN  THE  PRECEDING  PAGES. 


TABLE   I. 

Gravity  Correction  for  a  Barometric  Pressure  of  760  mm.,  for  each  Degree  of 
Latitude  /,  which  is  the  Argument  of  the  Table. 


L 

Correction. 

4- 

- 

Correction. 

i 

mm. 

Inches. 

mm. 

Inches. 

0° 

.98 

0.078 

90 

23 

•37 

0.054 

67 

I 

.98 

.078 

89 

24 

•33 

.052 

66 

2 

•97 

.078 

88 

25 

.27 

.050 

65 

3 

•97 

.078 

87 

26 

.22 

.048 

64 

4 

.96 

•077 

86 

27 

.16 

.046 

63 

5 

•95 

.077 

85 

28 

.11 

.044 

62 

6 

•94 

.076 

84 

29 

•05 

.041 

61 

7 

.92 

.076 

83 

30 

0.99 

•039 

60 

8 

.90 

•075 

82 

3i 

0-93 

•037 

59 

9 

.88 

.074 

81 

32 

0.87 

•034 

58 

10 

.86 

•073 

80 

33 

0.81 

.032 

57 

ii 

.84 

.072 

79 

34 

0.74 

.029 

56 

12 

.81 

.071 

78 

35 

0.68 

.027 

55 

13 

•  78 

.070 

77 

36 

0.61 

.024 

54 

14 

•75 

.069 

76 

37 

o.55 

.022 

53 

15 

•72 

.067 

75 

38 

0.48 

.Olg 

52 

16 

.68 

.066 

74 

39 

0.41 

.016 

51 

17 

.64 

.065 

73 

40 

0.34 

.014 

50 

18 

.60 

.063 

72 

41 

0.28 

.Oil 

49 

19 

•  56 

.062 

71 

42 

0.21 

.008 

48 

20 

•52 

.060 

70 

43 

0.14 

.005 

47 

21 

•47 

.058 

69 

44 

0.07 

.003 

46 

22 

.42 

.056 

68 

45 

0.00 

.OOO 

45 

NOTE. — The  correction  must  be  taken  according  to  the  sign  placed  under  the 
argument  /.  The  corrections  for  smaller  pressures,  at  some  altitude  above  sea- 
level,  must  be  diminished  in  proportion  to  the  pressures. 

473 


474 


APPENDIX. 


TABLE   II. 

The  Tension  of  Aqueous  Vapor  in  Saturated  Air  at  the  Temperature  T,  used  as 

an  Argument. 


T 

Tension. 

T 

Tension. 

T 

Tension. 

r 

Tension. 

T 

Tension. 

«F. 

Inches. 

o  p 

Inches. 

°F. 

Inches. 

o  T7 

Inches. 

°F. 

Inches. 

o 

0.045 

20 

0.109 

40 

0.246 

60' 

0.517 

80 

.O2I 

I 

0.047 

21 

0.114 

41 

0.256 

61 

0.536 

8l 

•055 

2 

0.049 

22 

0.119 

42 

0.266 

62 

0-555 

82 

.090 

3 

0.051 

23 

0.124 

43 

0.276 

63 

0-575 

83 

.126 

4 

0.054 

24 

0.129 

44 

0.287 

64 

0.595 

84 

.163 

5 

0.057 

25 

0.135 

45 

0.298 

65 

0.616 

85 

.201 

6 

0.059 

26 

0.141 

46 

0.310 

66 

0.638 

86 

•239 

7 

0.062 

27 

0.147 

47 

0.322 

67 

0.660 

87 

.279 

8 

0.065 

28 

0.153 

48 

0-334 

68 

0.683 

88 

.320 

9 

0.068 

29 

0.159 

49 

0-347 

69 

0.707 

89 

•363 

10 

0.071 

30 

0.166 

50 

0.360 

70 

0.732 

90 

.407 

ii 

0.075 

31 

0.173 

51 

0.374 

71 

0-757 

91 

•452 

12 

0.078 

32 

0.180 

52 

0.388 

72 

0.783 

92 

.498 

13 

0.081 

33 

0.187 

53 

0.402 

73 

0.810 

93 

•545 

14 

0.085 

34 

0.195 

54 

0.417 

74 

0.837 

94 

•594 

15 

0.088 

35 

0.203 

55 

0.432 

75 

0.865 

95 

.644 

16 

0.092 

36 

0.2II 

56 

0.448 

76 

0.894 

96 

•695 

17 

0.096 

37 

0.219 

57 

0.464 

77 

0.925 

97 

.748 

18 

O.IOO 

38 

0.228 

58 

0.481 

78 

0.956 

98 

.802 

19 

0.104 

39 

0.237 

59 

0.499 

79 

0.988 

99 

•857 

•C. 

mm. 

°C. 

mm. 

°C. 

mm. 

c. 

mm. 

•C 

mm. 

-  18 

1.  12 

—  7 

2.72 

+   4 

6.07 

+  15 

12.67 

+  26 

24.96 

17 

1.22 

6 

2-93 

5 

6.5I 

16 

13-51 

27 

26.47 

16 

.32 

5 

3-16 

6 

6-97 

17 

14.40 

28 

28.07 

15 

•44 

4 

3-41 

7 

7-47 

18 

15-33 

29 

29.74 

34 

•56 

3 

3.67 

8 

7-99 

19 

16.32 

30 

3I-5I 

13 

.69 

2 

3-95 

9 

8-55 

20 

17.36 

3i 

33-37 

12 

.84 

—  I 

4  25 

10 

9.14 

21 

18.47 

32 

35.32 

tfl 

•99 

0 

4-57 

ii 

9-77 

22 

19.63 

33 

37-37 

10 

2.15 

+  1 

4.91 

12 

10.43 

23 

20.86 

34 

39-52 

9 

2-33 

2 

5-27 

13 

11.14 

24 

22.15 

35 

41.78 

-       8 

2.51 

+  3 

5.66 

+  14 

11.88 

+  25. 

23-52 

+  36 

44.16 

APPENDIX. 
TABLE  III. 


47$ 


The  Decrease  in  Temperature  of  Ascending.  Air  for  each  100  Meters  of  Ascent 
for  the  different  Barometric  Pressures  P  and  Temperatures  r,  used  as  Argu- 
ments. Also  the  Weight  of  Aqueous  Vapor  in  a  Kilogram  of  Saturated  Air, 


T 

A  l.itiitflA   *•• 

P. 

-10° 

-5° 

0° 

5° 

10° 

15° 

20° 

25° 

3o° 

Altitude.* 

mm. 

0 

0 

0 

0 

0 

0 

0 

• 

0 

Meters. 

760 

0.74 

0.68 

0.64 

0.58 

o-53 

0.48 

0-43 

0.40 

0-37 

0 

700 

•73 

.66 

.63 

•  57 

•  51 

.46 

.42 

•  38 

.36 

660 

600 

.70 

•  63 

.60 

•54 

.48 

.43 

.40 

•36 

1897 

500 

.66 

.60 

.56 

-50 

•45 

.40 

•37 

3357 

400 

.62 

•55 

•51 

.46 

.41 

•  37 

5142 

300 

.56 

.49 

.46 

.42 

7550 

200 

.48 

.41 

•39 

10680 

Weight  of  Aqueous  Vapor  in  a  Kilogram  of  Saturated  Air. 


mm. 

gram. 

gram. 

gram. 

gram. 

gram. 

gram. 

gram. 

gram. 

gram. 

760 

1-7 

2.6 

3-8 

5-4 

7.6 

10.5 

14.4 

19.5 

26.3 

0 

600 

2.2 

3-2 

4.6 

6.8 

9.6 

13.3 

I8.3 

24.8 

1897 

400 

3-3 

4.8 

7.2 

10.2 

14.4 

20.0 

5142 

200 

6-5 

6.7 

10680 

*  Computed  with  the  temperatures  of  §  13. 


476 


APPENDIX. 


TABLE   IV. 

The  Heights,  in  meters,  of  Incipient  Condensation  in  ascending  currents  of  Air, 
for  the  Temperatures  r,  and  the  Depressions  of  the  Dew-point,  r  —  d,  in 
Centigrade  degrees,  used  as  arguments. 


J 

AIR  TEMPERATURES  r. 

35° 

30° 

25° 

20° 

15° 

10° 

5° 

0° 

-5° 

—  10° 

-15° 

1° 

128 

127 

127 

126 

126 

125 

125 

125 

125 

125 

125 

2 

255 

254 

253 

252 

251 

250 

250 

250 

250 

250 

250 

3 

382 

380 

379 

377 

376 

375 

375 

375 

395 

375 

375 

4 

509 

506 

505 

502 

50i 

500 

500 

500 

500 

500 

500 

5 

635 

632 

630 

627 

625 

624 

624 

625 

624 

624 

624 

6 

76l 

758 

755 

75i 

748 

747 

746 

748 

746 

748 

7 

886 

883 

879 

874 

871 

869 

868 

870 

868 

870 

8 

1012 

1009 

1003 

997 

993 

991 

99° 

991 

990 

992 

9 

H37 

H33 

1127 

1120 

IH5 

1113 

IIII 

III2 

III2 

1114 

10 

1262 

1257 

1250 

1242 

1236 

1234 

1232 

1232 

1233 

1235 

ii 

1387 

1382 

1374 

1364 

1357 

1355 

1352 

1351 

1352 

12 

I5H 

1506 

1497 

1485 

1478 

1476 

1472 

1470 

1470 

13 

1635 

1630 

1620 

1606 

1599 

1596 

1592 

1589 

1588 

14 

1759 

1754 

1743 

1727 

1720 

1716 

1711 

1708 

1705 

15 

1883 

1877 

1865 

1848 

1841 

1836 

1830 

1826 

1822 

16 

2005 

1999 

1985 

1969 

1962 

1956 

1950 

1945 

17 

2127 

2I2O 

2105 

2090 

2083 

2076 

2070 

2065 

18 

2249 

2241 

2225 

2211 

2203 

2196 

2190 

2185 

19 

2371 

2361 

2344 

2332 

2323 

2316 

2310 

2305 

20 

2493 

2480 

2463 

2452 

2443 

2435 

2430 

2425 

21 

2614 

2599 

2582 

2572 

2563 

2554 

2548 

22 

2734 

2718 

2700 

2691 

2683 

2672 

2665 

23 

2854 

2837 

2819 

28lO 

2802 

2790 

2681 

24 

2974 

2956 

2938 

2929 

2921 

2908 

2795 

25 

3093 

3075 

3056 

3048 

3040 

3025 

3009 

26 

3214 

3192 

3J73 

3165 

3158 

3i4i 

27 

3332 

3309 

3290 

3282 

3275 

3256 

28 

3450 

3426 

3407 

3399 

3391 

3371 

29 

3568 

3543 

3524 

3515 

3506 

3496 

30 

3685 

3660 

3640 

3631 

3621 

3600 

31 

3801 

3775 

3757 

3749 

3737 

32 

391? 

3891 

3874 

3867 

3854 

33 

4032 

4006 

399° 

3984 

397i 

34 

4M7 

4120 

4107 

4101 

4088 

35 

4261 

4235 

4223 

4218 

4205 

36 

4375 

4349 

4338 

4333 

37 

4488 

4462 

4452 

4448 

38 

4601 

4576 

4566 

4562 

39 

4713 

4690 

4680 

4686 

40 

4826 

4804 

4794 

4790 

41 

4939 

4918 

4908 

42 

5053 

5032 

5022 

43 

5168 

5146 

5136 

44 

5284 

5261 

5250 

45 

5400 

5376 

5364 

46 

55i8 

5492 

47 

5638 

5609 

48 

5759 

5727 

49 

5881 

5846 

50 

6005 

5966 

APPENDIX. 
TABLE   V. 


477 


Containing  several  functions  defined  and  referred  to  in  the  preceding  pages> 
useful  in  facilitating  the  computations  of  many  of  the  Formulae.  The 
functions  are  given  for  each  Fifth  Degree  of  the  Latitude  /,  used  as  an 
argument. 


I 

sin  / 

COS  / 

(0 

in  Meters. 

e 
s 

2  n  sin  / 

G 

0° 

0.00000 

I.OOOOO 

465.0 

0.00000000 

o.ooooooo 

o.oooo 

5 

.08716 

0.99619 

463.2 

130 

127 

0.0137 

10 

.17365 

.98481 

458.0 

258 

253 

.0273 

15 

.25882 

•96593 

449.2 

385 

377 

.  0406 

20 

.34202 

.93969 

436.9 

509 

499 

.0537 

25 

.42262 

.90631 

421.5 

629 

616 

.0664 

30 

.50000 

.86603 

402.7 

744 

729 

.0785 

35 

.57358 

.81915 

380.7 

853 

837 

.0901 

40 

.64279 

.76604 

356.3 

956 

937 

.1010 

45 

.70711 

.70711 

328.8 

1052 

1031 

.1111 

50 

.76604 

.64279 

298.9 

"39 

1117 

.I2O4 

55 

.81915 

.57358 

266.7 

1219 

"95 

.1287 

60 

.86603 

.50000 

232.5 

1288 

1263 

.I36l 

65 

.90631 

.42262 

196.6 

1348 

1322 

.1424 

70 

.93969 

.34202 

159.0 

1398 

1370 

-1477 

75 

.96593 

.25882 

I2O.4 

1437 

1408 

.1518 

80 

.98481 

.17365 

80.8 

1465 

1436 

-1547 

85 

.99619 

.08716 

40.6 

1481 

1453 

.1565 

90 

I.OOOOO 

o.ooooo 

oo.o 

0.00001487 

0.0001458 

O.I57I 

478 


APPENDIX. 


TABLE    VI. 

Height  in  Meters  AH  oi  a  Column  of  Pure  and  Dry  Air,  corresponding  to  a 
Millimeter  of  Barometric  Pressure,  at  different  Temperatures  and  Pressures, 

7993       T_ 
P     '   To 


Computed  by  the  Formula  AH '  = 


Barometric 
Pressure  in 
Millimeters. 

TEMPERATURE  BY  THE  CENTIGRADE  SCALE. 

—  10° 

-5° 

0° 

5° 

10° 

15° 

20° 

25° 

30° 

35° 

760 

10.13 

10.32 

10.52 

10.71 

10.90 

1  1.  1C 

11.29 

ii.  4 

ii  6 

11.87 

750 

10.27 

10.46 

10.66 

10.85 

11.05 

11.24 

11.44 

11.63 

ii.  8 

12.02 

740 

10.40 

10.60 

10.80 

II.  OO 

11.20 

H.39 

"•59 

11.79 

11.99 

12.  19 

730 

10.55 

io.75 

10.95 

H.I5 

n-35 

H-55 

H.75 

11.93 

12.  I 

12-35 

720 

10.70 

10.90 

II.  10 

11-30 

11.51 

11.71 

11.91 

12.12 

13.32 

12.52 

710 

10.85 

11.05 

11.26 

11.67 

11.68 

11.88 

12.08 

12.29 

12.49 

I2.7O 

700 

II.  OO 

II.  21 

11.42 

11.63 

11.84 

12.05 

12.26 

12.46 

12.67 

12.88 

690 

11.16 

H-37 

11.58 

II.80 

12.01 

12.22 

12.43 

12.64 

12.  80 

13.07 

•680 

11.32 

11-54 

«-75 

11.97 

12.  l8 

12.40 

12.61 

12.83 

13.05 

13.26 

670 

11.49 

11.71 

H-93 

12.15 

12.37 

12.58 

12.80 

13.02 

13.24 

13.46 

660 

11.67 

11.89 

12.  II 

12.33 

12.55 

12.78 

13-00 

13.22 

13.44 

13.66 

650 

11.85 

12.07 

12.30 

12.52 

12.75 

I2.97 

13-20 

13.42 

13.65 

13-87 

640 

12.03 

12.26 

12.49 

12.72 

12.96 

I3-I8 

13.40 

13.63 

13.86 

14.09 

630 

12.22 

12.45 

12.69 

12.92 

13.15 

13.38 

13.61 

13.85 

14.08 

I4.3I 

620 

12.42 

12.66 

12.89 

13.13 

13-36 

13.60 

13.84 

14.07 

14.31 

14-54 

610 

12.62 

12.86 

13-10 

13-34 

13.58 

13.82 

14.06 

14.30 

14-54 

14.78 

-600 

12.83 

13  08 

13.32 

13-57 

13.81 

14.05 

14.30 

14.54 

14.79 

15-03 

59° 

I3-05 

I3-30 

13-55 

I3-80 

14.04 

14.29 

14.54 

14.79 

15-Oij 

15.28 

580 

13.28 

13-53 

13.78 

14.03 

14.28 

14.54 

14.79 

15.04 

15.30 

15-54 

570 

I3-5I 

13-77 

14.02 

14.28 

14-54 

14.79 

15-05 

15.31 

15.56 

15.82 

560 

13-75 

14.01 

14.27 

14-53 

14.80 

15.06 

15-32 

15.58 

15.84 

16.10 

:550 

I4.OI 

14.28 

14-54 

I4.8l 

15.07 

15-34 

15.60 

15.87 

16.13 

16.40 

540 

14.26 

14-53 

14.80 

15.07 

15.34 

I5.6I 

15.89 

16.16 

16.43 

16.70 

530 

14-53 

14.80 

15.08 

15.36 

15.63 

15.91 

16.18 

16.46 

16.74 

17.  01 

520 

I4.8l 

15.09 

15.37 

15.65 

15.93 

16.21 

16.50 

16.78 

17.06 

17-34 

510 

15.10 

15-39 

15.67 

15.96 

16.25 

16.53 

16.82 

17.11 

17.39 

17.68 

500 

15.40 

15.69 

15.99 

16.28 

16.57 

16.86 

17.16 

17-45 

17.74 

18.04 

.490 

15-71 

16.01 

16.31 

16.61 

16.91 

17.21 

17-51 

17.81 

I8.IO 

18.40 

480 

16.04 

16.35 

16.65 

16.96 

17.26 

17.57 

17.87 

18.18 

18.48 

18.79 

470 

16.38 

16.70 

17.01 

17.32 

17.63 

17.94 

18.25 

18.56 

18.87 

19.18 

460 

16.74 

17.07 

17.38 

17.69 

18.01 

18.33 

18.65 

18.97 

19.28 

19.60 

450 

17.11 

17.44 

17.76 

18.09 

18.41 

18.74 

19.06 

19-39 

19.71 

20.04 

440 

17.50 

17-83 

18.17 

18.50 

18.83    19-16 

19.50 

19.83 

20.  16 

20.50 

430 

17.91 

18.25 

18.59 

18.93 

19.27    19.61 

19-95 

2;.  29 

20.63 

20.97 

420 

18.33 

18.68 

19.03 

19.38 

19.73    20.07 

20.42 

20.77 

21.12 

21.47 

410 

18.78 

19.14 

19.50 

19.85 

20.21 

20.57 

20.92 

21.28 

21.64 

21-  V9 

400 

19.25 

19.62 

19.98 

20.35 

20.71 

21.  08 

21.45 

21.  8l 

22.18 

22.54 

390 

19.74 

20.12 

2O.5O 

20.87 

2I.24i    21.62 

22.00 

22.37 

22-75 

23.12 

380 

20.26 

20.65 

21.03 

21.42 

21.  80 

22.19 

22.57 

22.96 

23-35 

23.73 

NOTE. — The  Barometric  Pressures  are  the  Barometer  Readings  corrected 
for  varying  gravity,  and,  strictly,  they,  as  well  as  the  Temperatures,  belong  to 
the  middle  of  the  column  AH.  The  Carbonic  Acid  in  the  air  makes  AH  a  very 
kittle  less,  and  the  Aqueous  Vapor  a  little  greater,  than  the  values  above. 


APPENDIX. 


479 


TABLE  VII. 

The  approximate  force  of  the  Wind,  /',  upon  a  square  foot  of  Normal  Surface, 
and  the  diameter  D  of  a  sphere  of  the  density  of  water  supported  in  the  air 
by  an  ascending  current,  for  the  several  Velocities  s  and  Barometric  Pres- 
sures P,  used  as  arguments. 


•S| 

BAROMETRIC  PRESSURES  P  IN  MILLIMETERS. 

fcjL 

760 

700 

600 

500 

400 

II 

r 

D 

f 

D 

P' 

D 

f 

D 

P' 

D 

pounds 

inches. 

pounds 

inches. 

pounds. 

inches. 

pounds. 

inches. 

pounds. 

inches. 

5 

O.I 

O.OI 

O.I 

O.OI 

O.I 

O.OI 

0.0 

O.OI 

0.0 

O.OI 

10 

0.3 

0.04 

0-3 

0.04 

0.2 

O.O4 

O.2 

0.03 

O.2 

0.03 

15 

0-3 

O.  IO 

0.6 

O.IO 

0.6 

0.09 

0-5 

0.07 

0.4 

0.06 

20 

1.2 

0.18 

i.i 

0.17 

I.O 

0.15 

0.8 

0.12 

0.7 

O.IO 

25 

I.g 

0.27 

1.8 

0.26 

1-5 

0.23 

1-3 

O.ig 

I.I 

0.16 

30 

2.7 

0.40 

2-5 

0-37 

2.2 

0.32 

0.27 

1.6 

0.22 

35 

3-7 

o.54 

3-5 

0.50 

3«O 

0.44 

2.6 

0-37 

2.1 

0.31 

40 

4.9 

0.70 

4-5 

0.65 

4.0 

0-57 

3-4 

0.48 

2.8 

O.4O 

45 

6.2 

0.89 

5-7 

0.83 

5-O 

0.72 

4.2 

0.62 

3-5 

0-51 

50 

7-6 

I.  IO 

7-  * 

I.  O2 

6.2 

0.99 

5-3 

0.76 

4-3 

0.63 

55 

9-2 

1-33 

8.6 

1.24 

7.1 

I.  II 

6.4 

0.88 

5-2 

0.75 

60 

II.  O 

1.58 

10.2 

1.47 

8.9 

1.28 

7.6 

.09 

6.2 

65 

12.9 

i  86 

12.  0 

1-73 

10.4 

1.51 

8.9 

.28 

7.3 

!o6 

70 

15-0 

2-15 

13-9 

2.00 

12.  1 

1.74 

10.3 

.49 

8-5 

•23 

75 

17.2 

2.47 

16.0 

2.30 

13-9 

2.00 

ii.  8 

•71 

9.8 

.41 

80 

19-5 

2.81 

18.2 

2.62 

I5.8 

2.28 

13-5 

-94 

n.  i 

.60 

85 

22.  0 

3  17 

20.5 

2-95 

I7.8 

2-57 

15-2 

2.18 

12.5 

,80 

90 

24.7 

3.56 

23-0 

3-31 

20.  o 

2.88 

17.0 

2-45 

14.1 

2.02 

95 

27.6 

3-97 

25.6 

3-70 

22.4 

3-22 

19.0 

2.74 

15-7 

2.26 

100 

30.5 

4.40 

28.4 

4.09 

24.7 

3.56 

21.0 

3.03 

17.4 

2.50 

These  functions  have  been  computed  from  the  formulae  of  §§  246,  247,  using 
the  temperatures  given  in  §  13,  corresponding  to  the  several  barometric  pres- 
sures. For  exceptionally  great  velocities,  these  functions  can  be  obtained  from 
those  above  by  taking  them  as  the  squares  of  the  velocities. 


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480 


APPENDIX.  481 

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29.  Selections  from  the  Works  of  Humboldt ;  by  John  Taylor. 

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32.  Quar.  Journal  Met.  Soc.,  London,  vol.  I,  p.  203. 

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34.  Philosophy  of  Storms  ;  by  James  P.  Espy,  A.M. 

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36.  Voyage  to  the  Southern  Seas,  vol.  n,  p.  283. 

37.  Notes  on  the  Meteorology  and   Physical  Geography  of  the  West 

Coast  of  Africa,  etc. ;  by  Commander  Edmund  George  Burke, 
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38.  The  Storm  and  Low  Barometer  of  December  8th  and  9th,  1886;  by 

Charles  Harding,  F.  R.  Met.  Soc.  Quar.  Jour.  Roy.  Met.  Soc.,  vol. 
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39.  Journal  of  the  Scottish   Meteorological  Society,  1873,  p.  66.     Also 

Quarterly  Journal  of  the  Meteorological  Society,  October  1877. 

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482  APPENDIX. 

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Octobre  de  1875  y  1876 ;  by  R.  P.  Benito  Vines,  S.  J. 

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51.  Contributions  to  Meteorology.     Seventh  Paper.     Sillimans  Journal, 

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52.  Observations  and  Researches  made  at  the  Hong  Kong  Observatory, 

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56.  The  Mean  Direction  of  Cirrus  Clouds  over  Europe.     Quar.  Jour. 

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INDEX. 


Abercromby.     Observations  of  upper  equatorial  currents  of  air,  127 
Phenomena  attending  the  approach  of  cyclones,  301 
Remarks  on  the  eye  of  the  storm,  312 
Thunder-storms,  451 
Acceleration,  9-44 
Air  —  (see  also  Atmosphere.) 
Dry,  i 

Dry  and  pure,  i 
The  density  of,  13 

Dynamical  heating  and  cooling  of  the,  20 
The  expansion  of,  24 
The  specific  heat  of,  25 
Weight  of  dry,  25 

Amount  of  work  done  by  heating,  26 
Heating  effect  of  compressing,  27 
Cooling  effect  of  expanding,  27 

Cooling  and  heating  of,  in  ascending  and  descending  currents,  27 
Ascending  and  descending  saturated,  30,  31 
Rates  of  decrease  of  temperature  of  saturated  ascending,   for  different 

temperatures  and  altitudes,  31 

Normal  rate  of  cooling  for  ascending  currents  of,  33 
Height  at  which  ascending  moist,  becomes  saturated,  33 
Stable  and  unstable  equilibrium,  34-39 
Relation  between  altitude  and  density  of,  39 
The  viscosity  of  the,  40 

Effect  of  the  general  motions  of  the,  upon  atmospheric  pressure,  133 
Interchanging  motions  of  the,  between  the  two  hemispheres,  141 
Conditions  of  the,  within  the  rain-belt,  167 

Great  tendency  of  heated  currents  of,  on  plateaus,  to  ascend,  198 
Outflow  of,  from  interior  Asia  in  winter,  206 
Anderson,  Dr.     Observation  on  direction  of  strong  winds  in  tornadoes,  397 

Observations  on  discontinuity  of  line  of  destruction  in  the  tornado 
of  April,  1883,  399 

485 


486  INDEX. 

Aqueous  Vapor — of  the  atmosphere,  16 

Distribution  of,  according  to  Dalton's  law,  17 
The  maximum  tension  of,  17 
Distribution  of,  101,  102 
Areas,  The  principle  of  the  preservation  of,  54-59 

The  principle  of  equal,  in  motions  on  the  earth's  surface,  65-70- 
Application  of  the  principle  of  equal,  67 

Principle  of  the  preservation  of,  applied  to  vertical  currents,  116 
Atmosphere,  Constitution  and  nature  of  the,  i 
Composition  of  the,  I 
Arrangement  of  the  constituents  of  the,  4 
Pressure  of  the,  9 
The  height  of  a  homogeneous,  14 
Hypothetical,  14 

Law  of  the  heights  of  homogeneous,  15 
Tables  of  pressures  of  the,  at  various  heights,  15 
The  general  circulation  of  the,  89-162 
Superior  limit  of  the,  89 

General  circulation  of  the,  without  rotation  of  the  earth,  102-106 
Neutral  plane  in  the  motions  of  the,  105 
Vertical  circulation  of  the,  105 

General  circulation  of  the,  with  rotation  of  the  earth,  106-133 
Principle  of    preservation    of  areas  applied   to  vertical  currents 

of  the,  116 

Complexity  of  the  circulation  of  the,  119 

Observed  circulation  of  the,  compared  with  the  theoretical,  121 
Easterly  currents  of  the  upper  strata  of  the,  121 
Annual  inequality  in  the  easterly  and  westerly  motions  of  the,  131 
Effect  of  the  general  motions  of  the  air  upon  the  pressure  of  the, 

133-145 

Effect  of  the  upward  expansion  ofjthe,  on  the  isobaric  surfaces,  134 
General  distribution  of  pressure  of  the,  along  a  meridian,  136 
Equatorial  depression  of  pressure  of  the,  136 
The  greatest  pressure  of  the,  at  the  earth's  surface,  136 
Zones  of  high  and  low  pressure  of  the,  on  the  earth's  surface,  139 
Table  showing  decrease  of  pressure  of  the,  from  the  tropics,  140 
Annual  inequality   of  pressure  of  the,  due  to  differences  in  tem- 
perature gradient,  141 

Interchanging  motions  of  the,  between  the  two  hemispheres,  142 
Annual  inversion  of  pressure  gradients  of  the,  142 
Annual  mean  pressure  of  the,  and  annual  inequality  for  various 

latitudes,  143 
Comparison   with  theory  of  the  observed  pressure  of  the,  and  its. 

inequalities,  144 

Annual  inequality  of  the  pressure  of  the,  greater  in  the  northern 
than  in  the  southern  hemisphere,  144 


INDEX.  487 

Atmosphere,  Study  of  the  general  motions  and  pressures  of  the,  148 

Necessity  for  excess  of  polar  and  equatorial  over  east  and  west 

motions  of  the,  in  case  of  much  friction,  150 
No  east   and  west  motion  of  the,  at  the  earth's  surface  on  the 

parallel  of  maximum  pressure,  153 
Summary  and  graphic  representation  of  the  motions  and  pressure 

of  the,  154-156 

Climatic  influence  of  the  general  circulation  of  the,  163 
Vertical  circulation  of  the,  in  the  calm-belt,  167 

Balloon  ascensions,  7 
Barnard  tornado,  389 

Barometer,  The  reduction  of  the,  to  sea-level  and  for  latitude,  10 
"  Pumping"  of  the,  448 
Vines'  remarks  on  pumping  of  the,  449 
Barometric  gradient,  83 

Mathematical  expressions  for  the,  83-85 
Conditions  for  making  the,  vanish,  137 
Vertical  distribution  of,  138 

Barometric  pressure,  Zones  of  high  and  low,  on  the  earth's  surface,  139 
Effect  of  the  zones  of  high,  150 
Areas  of  high,  342-346 
Bora,  The,  331 

Boue.     Observation  of  the  hollow  centre  of  water-spouts,  419 
Boyle  and  Mariotte's  Law,  2 

Deviation  from,  3 

Brault's  charts  of  wind  directions,  184 

Brown,  J.  Allen.    Tables  of  inclination  of  winds  in  cyclones,  265 
Buch,  Leopold.     Remarks  on  winds  at  Teneriffe,  126 
Buchan,   Isothermal  charts  of,  100 

Reference  to  temperature  charts  of,  180 
Winter  thunder-storms  at  Stykkisholm,  471 
Burke,  Observations  of  sea-breezes  on  coast  of  Guinea  by,  222 
Buy-s  Ballot's  Law  for  direction  of  wind,  263 

Calms  and  calm-belts,  149 

Calms,  Surface,  in  cyclones  (see  also  under  Cyclones),  257 

Calm-belts  and  calms,  149 

Annual  oscillations  of  the,  156-162 
Calm-belts,  Mean  position  of  the  equatorial,  a  little  north  of  the  equator,  157 

Causes  of  the  equatorial,  158 

Limits  and  oscillations  of  the  equatorial,  159 

Oscillations  of  the,  of  the  Pacific  Ocean,  162 

Weather  under  the  cloud-ring  of  the,  168 

Calm-belts,  Lower  temperature   in  the,  according  to  Espy,  Wilkes,  and  Hum- 
boldt,  169 


INDEX. 

Peculiarities  of  climate  within  range  of  oscillation  of  rain-belt  and, 

169,  170 

Regularity  of  atmospheric  phenomena  in  the,  177 
Centrifugal  force,  and  gyratory  velocity,  47 
Ratio  of,  and  gravity,  48 
Mathematical  expression  for,  53,  54 
in  motions  on  the  earth's  surface,  60-65 
of  the  earth's  rotation,  61 
Horizontal  component  of,  62 
Acceleration  of  the,  at  the  equator,  63 
General  expression  for  the  horizontal  component  of,  64 
Barometric  gradients  depending  upon,  85 
Charles  and  Gay-Lussac,  Laws  of,  3,  4 
Charles,  Deviation  from  the  law  of,  3 
Chinook  winds,  Description  of,  334 

Investigation  of,  by  Harrington,  Dawson,  334,  335 
Christison,  Investigation  of  the  pamperos  of  Uruguay  by,  329 
Clayton,  Observations  of  pressure  gradient  in  thunder-storms  by,  465 
Climate,  Effect  of  the  general  circulation  of  the   winds  on  the,  of  the  higher 

and  lower  latitudes,  163,  164 
Characteristics  of  a  continental,  181 

Differences  of  the,  on  eastern  and  western  coasts,  181,  182 
Influence  of  mountain  ranges  on,  183-192 

Clouds,  Resultant  directions  of  the  motions  of,  at  Toronto,  Canada,  122 
Directions  and  frequency  of  cirrus,  at  Zi-ka-wei,  122,  308 
Motions  of  the,  at  Colonia  Tover,  Venezuela,  123 
Remarks  of  Ley  on  the  motions  of  cirrus,  121,  308 
Height  at  which,  are  formed,  239 
Formation  and  disappearance  of,  239 
Mares'  tails,  300 
Cloud-bursts,  Account  of,  429-434 

in  the  Hollidaysburg,  Pa.,  tornado,  observed  by  Espy,  431 
Accounts  of,  at  Catskill,  N.  Y.;  Ft.  Keogh,  Mont.; and  Ft.  Eliott, 

Tex.,  431,  432 

Down-pour  of  water  from,  430,  432 
Coffin,  Prof.,  Velocity  of  resultant  motion,  for  the  year,  of  the  air  in  the  U.  S., 

by,  129 

Annual  inequality  of  resultant  wind  velocities  in  U.  S. ,  by,  133 
Prevailing  wind  directions,  by,  186 

Collins,  Lieut.     Observations  of  rainfall  at  Nicaragua,  175 
Cold-waves,  Woodruff's  investigation  of,  in  U.  S.,  322 
as  trough  phenomena  of  cyclones,  327 
Explanation  of,  in  Mississippi  Valley,  by  Hinrichs,  329 
Condensation,  Latent  heat  given  out  in,  29 
Continuity,  The  condition  of,  94 


INDEX.  489 

Curvature,  Radius  of,  48 
Cyclones,  226 

Definition  and  general  causes  of,  227 

Vertical  circi:  ation  in,  227-240 

Sustaining  power  of  the  vertical  circulation  in,  230,  231 

Vertical  temperature  gradients  in,  229,  230 

Stable  and  unstable  atmosphere  in,  229 

A  cause  of  the  vanishing  of  the  force  of,  234 

Ascending  and  descending  currents  in,  due  to  the  various  temperature 
gradients,  234-239 

Dew-point  in  the  vertical  circulation  of,  237 

Vertical   circulation   in,  with   change    of    temperature   gradient   with 
height,  240 

Irregularity  of  temperature  gradient  in,  240 

Undefined  outer  limit  to,  241 

Gyratory  motion  of,  241 

Rotation    of  the  earth  on  its  axis  the  cause  of  the  gyratory  motion 
in,  242 

Gyratory  motion  of  the  air  from  right  to  left  in,  242 

Inflow  of  air  below  and  outflow  above  in,  243 

And.     Definition  of,  243 

Application  of  the  principle  of  the  preservation  of  areas  in,  244 

Centrifugal  and  centripetal  forces  in,  244 

Motion    of    limited,  compared  with  the  atmospheric    motions  of  a 
whole  hemisphere,  246 

Motions  toward  the  centre  in,  247 

Conditions  which  might  prevent  vertical  circulation  in,  248 

Momentum  and  inertia  of  the  air  in,  250 

Law  of  decrease  of  the  relative  velocities  of  the  gyrations  above  and 
below  in,  250 

Relative  gyratory  velocities  in,  and  anti-cyclones,  250 

Atmospheric  pressure  in,  251 

Effect  of  the  upward  expansion  of  the  air  on  the  pressure  in,  252 

Gyratory  velocity  and  barometric  gradient  in,  252 

The  region  of  greatest  pressure  in,  254 

Pressure  distribution  above  the  earth's  surface  in,  254 

Resultant  motions  in,  255 

Definition  of  the  inclination  in,  255 

The  ring  of  highest  pressure  in,  256 

Effect  of  the  viscosity  of  the  air  upon  the  gyratory  and  vertical  circu- 
lation in,  256 

Ratio  between  the  radial  and  gyratory  velocities  near  the  centre  of,  257 

Surface  calms  in,  257 

Graphic  representation  of  motions  and  pressures  in,  258-261 

Relative  direction  of  upper  and  lower  currents  in,  261 


49°  INDEX. 

Cyclones,  Comparison  of  the  theory  of,  with  observation,  261-271 

Inclination  of  the  wind  at  the  earth's  surface  in,  according  to  Redfield^ 
Buys-Ballot,  Ley,  Loomis,  Brown,  Vines,  Hildebrandsson,  Hoff- 
meyer,  Spindler,  Toynbee,  and  Piddington.  262-265 

Inclination  of  winds  in,  according  to  Loomis,  264 

Difference  of  inclination  of  winds  in  front  and  rear  of,  265 

preceded  and  followed  by  unusually  high  barometer,  according  to 
Redfield  and  Espy,  269,  270 

Upper  currents  of  air  in,  according  to  Ley,  Hildebrandson,  and  Loo- 
mis, 270-271 

Gradual  enlargement  of,  273,  274 

Dimensions  of  the  violent  part  of,  according  to  Redfield,  Piddington, 
and  Reid,  274 

Progressive  motion  of,  275-286 

Loomis'  tables  of  the  motions  of  centres  of,  in  U.  S. ,  Atlantic  Ocean, 
and  Europe,  276 

Polar  tendency  of,  in  lower  latitudes,  277 

Motions  of,  on  east  coasts  of  U.  S.,  China,  S.  Africa,  and  at  the  Fiji 
Islands,  278 

Parabolic  form  of  the  path  of,  279 

Direction  and  velocity  of  westwardly  moving,  according  to  Loomis,  279 

Paths  of,  in  various  quarters  of  the  globe,  280 

Table  of  annual  period  of  frequency  of,  in  several  seas,  282 

Cause  of  the  more  rapid  progress  of,  in  U.  S.  than  in  Europe,  283 

Aqueous  vapor  in,  283 

Effect  of  differences  of  temperature  on  polar  and  equatorial  sides  of,. 
284,  285 

Effect  of,  upon  the  isotherms,  285 

,  Veering  and  backing  of  the  wind,  and  changes  of  pressure  and  tempera- 
ture in,  287-292 

Phenomena  attending  the  passage  of,  288 

Changes  of  wind  on  the  north  and  south  side  of,  during  the  eastward 
passage,  289 

Backing  and  veering  of  the  wind  in,  289 

Preponderance  of  veering  winds  in,  in  the  middle  latitudes  of  U.  S. 
and  Europe,  289 

Passage  of,  in  the  southern  hemisphere,  290 

Line  squalls  in,  290 

Loomis'  results  of  inclination  and  velocity  of  winds  in  the  four  quad- 
rants of,  291 

Ellipticity  of  the  isobars  in,  291 

of  Aug.  2,  1837,  at  St.  Thomas,  292 

Typhoon  at  Manilla,  Nov.  5,  1882,  295 

of  Cienfuegos  on  Sept.  5,  1882,  297 

Rain  and  cloud  areas  in,  298-303 

Form  and  position  of  rain  areas  in,  according  to  Loomis,  299 


INDEX.  491 

Cyclones,  Form  and  position  of  cloud  areas  in,  300 
Cirrus  clouds  as  precursors  of,  300 
with  little  rain  according  to  Loomis,  301 
Phenomena  attending  the    approach  of,   according  to  Abercromby, 

Vines,  and  Doberck,  301,  302 
Phenomena  after  the  passage  of,  302 

Relations  between  the  progressive  velocities  of  the  air  and,  304 
v      Dangerous  side  of,  307 

Wind  velocities  and  inclinations  at  Mt.  Washington  in,  according   to 

Loomis,  308 
The  "  eye  of  the  storm"  or  "bull's-eye"  in,  as  remarked  on  by  Dove, 

Captain  Salis,  Dr.  Malcolmson,  Abercromby,  311,  312 
Secondary,  315-317 
Occurrence  of  secondary,   in  the  southern  and  eastern  quadrants  of 

primary  cyclones,  316 

Showery  weather  produced  by  secondary,  317 
Stationary,  318-322 

Geographical  positions  of  some  stationary,  322 
with  cold  centre,  337-342 
Cause  of,  with  cold  centre,  337 
The  poles  the  centres  of,  with  cold  centre,  338 
with  cold  centre  may  or  may  not  have  a  minimum  pressure  at  the 

centre,  339 

with  cold  centre  in  Europe,  Asia,  and  N.  America,  340 
Difficulty  of  locating  the  centres  of,  341 
and  tornadoes  compared,  347 
Relation  between,  and  thunderstorms,  467-470 

Octants  of,  containing  least  and  greatest  number  of  thunder-storms,  468 
Cyclonic  gyrations,  243 

Anti-,  gyrations,  244 

gyrations  caused  by  any  given  temperature  disturbance  are  most  violent 

near  the  poles,  and  vanish  at  the  equator,  244 
Resultants  of,  and  progressive  motions,  303-311 

Dalton's  law,  i 

Arrangement  of  constituents  according  to,  6 
Dampier.     Remarks  on  land-  and  sea-breezes,  221 
Danckelman.     Table  of  rainfall  on  the  Congo,  172 
Davis.     Thunder-storms  in  New  England,  450 
Dawson.     On  the  Chinooks,  335 
Defecting  force  of  the  earth's  rotation,  77 

Effect  of  the,  of  the  earth's  rotation  on  projectiles  fired  upward,  87; 
Defranc.     Description  of  small  water-spouts,  416 

Remarks  on  times  of  occurrence  of  water-spouts,  441 
Delphos  tornado,  388 
Density,  Relative,  of  gases,  6 


-492  INDEX. 

Density,  Relation  between  changes  of  altitude  and,  39 
Deviation  of  a  rifle-ball  due  to  the  earth's  rotation,  86 

due  to  the  earth's  rotation  of  a  projectile  describing  a  parabolic  curve,  87 
Dew-point,  18,  401 
Dines.     Size  of  rain-drops,  380 
Doberck.     Observations  of  typhoons  in  China  Sea  and  Philippine  Isles,  268 

Phenomena  attending  the  approach  of  cyclones,  302 
Dove.     Tables  of  the  Pacific  trades,  161 

Cylones,  289,  292 

Cyclone  of  Aug.  2,  1837,  at  St.  Thomas,  292 

Remarks  on  eye  of  the  storm,  311 

Earth's  rotation,  Deflecting  force  of  the,  77-88 

Elementary  proof  of  the  effects  of,  78 

Illustration  of  the  effects  of,  79 

Deduction   of    absolute   amount   of    deflecting    force  due   to, 

80,  8 1 

Numerical  value  of  the  effects  of,  on  rivers,  81 
Numerical  computation  of  the  effects  of  the,  on  railroad  trains,  82 
Effect  of  the,  on  tornadoes,  352 

Effendi  Emin.     Rainfall  observed  in  the  travels  of,  from  Mreili  to  Rubaga,  174 
Elliot.     Thunder-storms  in  India,  450 
Energy,  potential,  kinetic,  and  thermal,  21 

The  conservation  of,  23 
Equilibrium,  General  principles  of  stable  and  unstable,  34  -36 

Vertical   distribution  of  temperature  causing  stable  and  unstable, 

35,  36 

Indifferent  state  of,  37 
Espy.     Easterly  motion  of  the  upper  currents,  121 

Remarks  on  low  barometric  pressure  in  the  southern  hemisphere,  140 
Lower  temperature  in  the  calm-belt,  169 
Remarks  on  the  northwest  monsoon,  208 
Remarks  on  the  northern  monsoon,  209 
Sudden  rise  of  the  barometer  preceding  storms,  270 
Researches  on  the  ellipticity  of  isobars  in  cyclones,  291 
on  the  foehn,  332 
Formation  of  a  cloud,  402 
Motions  of  the  low  clouds  in  a  hurricane,  410 
Observations  of  cloud-bursts,  430,  431 
Whirlwinds  produced  by  great  fires,  443 
Evaporation,  Daily  amount  of,  within  the  tropics,  164 

Falling  bodies,  45 

Ferrari.     Thunder-storms  in  Italy,  451,  455 

Origin  of  thunder-storms,  456 
Finley.     Account  of  tornadoes  of  May  29  and  30,  1879,  386-389 


INDEX.  493; 

Finley.     Width  of  the  path  of  destruction  of  tornadoes,  390 
Direction  of  the  rotary  motion  of  tornadoes,  395 
Velocity  of  progression  of  tornadoes,  395 
Direction  of  progressive  motion  of  tornadoes,  396 
Intermittent  action  of  the  Lee's  Summit  tornado,  407. 
Hail  in  tornadoes,  420 

The  times  of  greatest  frequency  of  tornadoes,  441 
Thunder-storms  in  tornadoes,  450 
Fluids,  Motions  of  inelastic,  90 
Flow  of,  90 
Pressures  in,  91 

Motions  in,  of  uniform  density,  90 
Motions  in,  of  different  densities,  91 
Motion  of,  in  canals  of  definite  lengths,  92 
Continuity  in  the  motions  of,  94 
Frictional  resistances  in  the  motion  of,  94 
Oscillatory,  interchanging  horizontal  motions  of,  96 
Orbit  of  particles  of,  moving  in  closed  canals,  97 
Motions  of,  in  wedge-shaped  canals,  94 
Motions  of,  in  the  open  ocean  from  equator  to  pole,  97 
Foehn,  332-335 

Explanation  of,  by  Espy  and  Hahn,  332,  333 
Force  or  pressure,  12 

Centrifugal,  42-45 

Formula  for  relative  gyratory,  59 

Mathematical  expression  for  the  deflecting,  64 

Resultants  of  the  two,  and  motions,  71 

The  deflecting,  not  a  real  force,  73 

Mathematical  expression  for  deflecting,  72 

Deflecting,  general  remarks  on,  73-74 

Torsional,  arising  from   the   effects  of  the  earth's  rotation  on  motion* 

caused  by  temperature  gradients,  113 

Motions  due  to  the  actions  of  a  central,  242  [244 

Centrifugal  and  centripetal,  in  cyclones  arising  from  pressure  gradients, 
Freezing,  The  reduction  to,  10 
Plane  of  incipient,  30 

Gases,  Elasticity  of,  2 

Specific  volume  of,  2 

The  relation  of  pressure  and  volume  in,  2 

Kinetic  theory  of,  2 

Relation  of  volume  and  temperature  in,  3 

at  low  pressure.     Mendeleef's  experiments,  & 

Relative  density  of,  6 
Gay-Lussac  and  Charles'  law,  3,  4 
Gentry  County  tornado,  389 


494  INDEX. 

•Glaisher.     Balloon  ascents,  232 

•Gould,  Dr.     Isothermal  charts  of  southern  S.  America,  ic,2 
'Gradient,  Measure  of  the,  49 
Ascending,  49 
Relation  between  the,  the   gyratory  velocity  and   distance   from   the 

centre,  50 

on  a  railway  curve,  51 
between  the  two  banks  of  a  river,  51 
Linear,  of  an  isobaric  surface  at  various  altitudes  due  to  difference  of 

temperatures,  103 

Change  of,  with  change  of  altitude,  104 
General  expression  of  barometric,  corresponding  to  any  given  velocity 

in  any  direction,  135 

Table  of  barometric,  for  various  latitudes,  143 
'Gravity,  The  force  of,  9 

The  reduction  to  standard,  10 
Ratio  of  centrifugal  force  and,  48 
Gyratory  velocity,  46 

Equation  for  the  absolute,  67 

Its  effect  on  pressure  (see  also  under  Tornadoes),  508-521 
Gyratory  motion,  52 

in  cyclones  (see  also  under  Cyclones),  241 

Hadley's  principle,  68 

principle  compared  with  the  author's,  69 

remarks  on  motions  and  counter- motions  of  the  atmosphere,  117 
Hagen,  Experiments  on  wind,  velocity,  and  pressure,  373 
Hail,  Theory  of  the  formation  of,  420-422 
-storms,  420^-429 

-stones,  Shape  of.     Hinrichs,  428 

-falls  in  Lee's  Summit,  Delphos,  and  Lincoln  tornadoes,  428 
Abnormal  fall  of,  at  Ft.  Elliott,  432 
Theory  of  the  formation  of  chunks  of,  434 
Hann.     Isothermal  charts,  100 
on  the  foehn,  333 

Reference  to  description  of  the  Sirocco,  337 

Harding.     Account  of  storm  in  the  British  Isles,  Dec.  8  and  9,  1886,  261 
Harrington  on  chinooks,  334 

Hazen,  Location  of  thunder-storms  with  reference  to  cyclonic  areas,  470 
Heat,  The  unit  of,  23 

The  mechanical  equivalent  of,  23 

Capacity  of  the  atmosphere  for,  compared  with  that  of  the  ocean,  163 
Relative  amounts  of,  transferred  by  atmospheric  and  oceanic  circulation,  164 
Latent,  of  condensation  in  the  calm-belt  strengthens  the  trade-winds,  167 
Hildebrandsson.     Observations  on  the  inclination  of  winds  in  the  front  and  rear 
of  cyclones,  267 


INDEX.  495 

Hildebrandsson.     Observations  on  the  upper  currents,  271 

Direction  of  cirrus  clouds  over  stationary  cyclones,  320 
Himalayas,  Mountain  winds  in  the,  223 
Hinrichs.     Shape  of  hailstones,  428 

Observations  of  storm  front  by,  454 

Hoffmeyer.     Observations  on  inclination  of  winds  in  cyclones,  265 
Hooker,  Dr.     Rainfall  in  Khasia,  205 
Horner.     Diameters  of  water-spouts,  408 
Houry,  Mr.     Description  of  hailstones,  425 
Humboldt.     Lower  temperature  in  the  calm-belt,  169 

Wet  and  dry  seasons  in  equatorial  Mexico,  176 

Wet  and  dry  seasons  in  S.  America,  177 

Sand  spouts  on  the  Orinoco,  444 
Humidity,  Relative,  19 

Average  relative,  for  the  earth's  surface,  IO2 
Hutton.     Experiments  on  the  resistance  of  air,  377 

Irving  tornado,  387 

isobaric  surfaces,  General  forms  of  the,  139 

Isothermal  charts,  Hann's,  Buchan's,  100 

Dr.  Gould's,  of  southern  S.  America,  192 

Jamaica,  Strongest  sea-breezes  at,  199 

Kerhallet,  Table  of  limits  of  Pacific  trade-winds,  162 

Khasia,  India.     Enormous  rainfall  in,  204 

Klossovsky.     Table  of  thunder-storms  in  Russia,  469 

Koppen.     Investigation  of  thunder-storm  of  Aug.  9,  1881,  in  Germany,  465 

Krakatoa,  Eruption  of,  124 

Land-  and  sea.-breezes  (see  also  tinder  Sea-breeze),  219 

breeze  often  comes  off  with  dangerous  squalls,  222 

Laplace.     Increase  of  the  temperature  in  the  barometric  formula  of,  102 
Laughton.     Remarks  on  sand  carried  to  sea  from  the  African  desert,  129 

Remarks  on  westerly  winds  in  both  hemispheres,  132 
Law,  Boyle  and  Mariotte's,  2 

Charles  and  Gay-Lussac,  3 

of  Boyle  and  Charles  combined,  expressed  mathematically,  3 
Lecoq.     Balloon  ascensions  in  a  thunder-cloud,  426 
Lee's  Summit  tornado,  386 
Ley.     Easterly  motion  of  the  upper  currents,  121 

Values  for  the  average  angle  of  inclination  of  the  winds  in  cyclones,  203 
Table  showing  directions  of  surface  and  upper  currents  in  cyclones,  264 
Cirrus  cloud  observations  by,  308 

Loomis.     Average  wind  velocities  for  U.  S. ,  Northern  Europe,  Southern  Asia, 
and  West  Indies,  130 


INDEX. 

Loomis.     Chart  of  mean  annual  rainfall,  166,  188 
Inclination  of  the  winds  in  cyclones,  255 
Investigation  of  winds  on  Mt.  Washington,  272 
Table  of  movement  of  cyclone  centres,  276 
Results    concerning    direction    and   velocity   of   westwardly   moving 

cyclones,  279 
Results  of  inclination  and  velocity  of  winds  in  the  four  quadrants  of  a 

cyclone,  291 

Researches  on  the  ellipticity  of  isobars  in  cyclones,  291 
Investigation  of  the  Manilla  typhoon  of  Nov.  5,  1882,  295 
Form  and  position  of  rain  areas  in  cyclones,  299 
Cyclones  with  little  rain,  300 
Results  of  wind  velocities  and  inclinations  for  the  four  quadrants  at 

Mt.  Washington  in  the  passage  of  cyclones,  308 
Relation  of  high  barometer  to  cyclones  in  the  U.  S.,  343-354 
Determination  of  the  coefficient  of  resistance  of  air,  372-377 
Diameter  of  water-spouts,  408 

Malcolmson.     Remarks  on  eye  of  the  storm,  312  [*59 

Maury.     Table  of  northern  limits  of  the  N.E.  trade-wind  in  the  Atlantic  Ocean, 

Weather  under  the  cloud-ring  of  the  equatorial  calm- belt,  168 
Mendeleef.     Experiments  on  Boyle's  law,  3 

Experiments  on  gases  at  low  pressure,  6 
Mistral,  The,  331 
Moisture,  Capacity  of  air  for,  28 

The  effect  on,  of  cooling  the  air,  29 
Moments  of  couple,  117 

Monsoons  and  land-  and  sea-breezes,  192-225 
Monsoon,  Definition  of,  and  character,  193 

Dependence  of,  upon  temperature  differences  or  gradients,  194 

Similarity  of,  and  land-  and  sea-breezes  on  small  islands,  195 

Dependence  of  the  strength  of  the,  on  the  nature  of  the  surface  of 
the  continent,  195 

Greatest,  found  adjacent  to  high  mountain  ranges,  196 

Influence  of  hot,  low,  level  countries  not  great  in  winter,  196 

S.  W. ,  of  Indian  Ocean,  called  the  monsoon,  200 

Great  strength  of  the,  in  Arabian  Sea,  201 

Effect  of,  on  the  southern,  eastern,  and  northern  coasts  of  Asia,  203, 

The  wet,  of  western  India,  205 

Northeast,  Winter,  and  Dry,  207 

in  Norway,  208 

Comparative  strength  of  N.E.  and  S.W.,  207 

winds  of  the  northern  Siberian  coast,  207 

Northwest,  208 

Northern,  209          | 

influence  in  Australia,  209,  210 


INDEX.  497 

Monsoon,  Climatic  influence  of  the  summer,  in  Australia,  210,  211 
Climatic  effect  of  the  winter,  in  Australia,  212 
of  Africa,  212 

The  southwest,  of  Africa,  213 
winds  in  central  Africa,  214 
of  N.  America,  214 

influences  in  N.  America  in  summer,  215 
influences  in  N.  America  in  winter,  216 
influences  in  Central  America  and  Mexico  in  summer,  216 
influences  on  the  west  and  northern  coast  of  N.  America,  217 
of  South  America,  217 
influences  over  Brazil,  218 

influences  in  Chili,  Peru,  and  at  Cape  Horn,  219 
Motions  of  bodies  relative  to  the  earth's  surface,  42 
in  a  groove,  48-59 

on  the  earth's  surface,  centrifugal  force  in,  60 
The  principles  of  equal  areas  in,  on  the  earth's  surface,  65 
Relative,  between  the  equator  and  the  pole,  68 
Resultants  of  the  two  forces  and,  71 
where  the  centre  of  force  is  not  the  pole,  75-77 
Uniform,  over  the  earth's  surface  without  friction,  86 
Frictional  resistances  in  the,  of  fluids,  94 
of  a  fluid  in  a  wedge-shaped  canal,  94 
of  a  fluid  in  the  open  ocean  from  equator  to  pole,  97 
Remarks  on  general,  of  the  atmosphere  and  forces  producing  them,  109 
Vertical,  downward  in  the  higher  latitudes  and  upward  in  the  lower 

latitudes,  112 

Annual  inequality  in  the  east  and  west  components  of,  115 
Resultant  direction  of,  for  various  altitudes  and  latitudes,  120 
Gyratory  in  cyclones,  241 

of  water  flowing  out  at  the  centre  of  a  shallow  basin,  242 
Resultants  of  cyclonic  and  progressive,  303-311 
Mount  Washington,  Winds  at,  127 

Washington,  Annual  equality  of  winds  at,  130          f 
Alibut  (near  Irkutsk),  Winds  at,  127 
Carmel,  111.,  tornado,  383 
Mountain  ranges,  Climatic  influences  of,  183,  184 

Effect  of,  on  adjacent  temperatures  and  rainfall,  188 

Newton.     Experiments  on  resistance  of  the  atmosphere  to  falling  bodies,  375 
Northers,  Cold-waves  and,  in  cyclones  (see  under  Cyclones),  322-329 

Extracts  from  an  account  of,  in  Texas,  by  Solomon  Sias,  325-327 

Wet  and  dry,  328 

Cloud  appearance  preceding,  328 

Ocean,  Pilot  chart  of  the  Atlantic,  159 


498  INDEX. 

Ocean,  Table  of  the  limits  of  the  trade-winds  in  the  Pacific,  162 
Olmsted.     Whirlwinds  produced  by  great  fires,  441 

Pamperos,  329-331 

Christison's  investigation  of  the,  of  Central  Uruguay,  329 
Similarity  of,  and  northers,  330 
Panama,  Wet  and  dry  seasons  at,  175 

Piddington.     Remarks  on  the  results  of  the  inclination  of  the  winds  in  cyclones, 
Remarks  on  dimensions  of  the  violent  part  of  cyclones,  274          [267 
Remarks  on  the  "  eye  of  the  storm,"  312 
Pike's  Peak,  Winds  at,  125 

Annual  inequality  of  winds  at,  126 

Plantamour.     Inversion  of  temperature  at  St.  Bernard  in  winter,  346 
Pressure,  Standard,  2 

Decrease  of,  in  the  vertical,  8 

Barometric,  10 

Unit  of,  12 

Observed,  at  various  altitudes,  16 

Lateral,  of  a  railroad  car,  49 

Causes  of  change  of  barometric,  or  pressure  gradient  at  the  earth's 

surface,  134 
Area  of  low,  255 

Relation  of,  and  velocity  of  the  air,  377 
Prjivalsky.     Observation  of  winds  in  Thibet,  203 

Quetelet.     Observations  on  upper  and  lower  currents  of  air,  266 

Radius  vector,  54 

Rain,  Monthly  probability  of,  at  Rubaga,  173 
Size  of  drops  of,  380,  433 

Size  of  drops  of,  an  indication  of  velocity  of  ascending  currents,  381 
Rain-belt,  Oscillation  of  the  middle  line  of  the,  in  South  America  and  Isthmus  of 

Panama,  173 

Rainy  and  dry  seasons  at  Greytown,  Nicaragua,  observed  by  Commander  Reed, 
in  equatorial  Mexico,  176  [174 

at  Panama,  175 

on  the  Orinoco  and  Amazon  rivers,  177 

Rainfall,  Woeikoff's  and  Loo  mis'  charts  of  mean  annual,  166 
Table  of  average  monthly,  on  the  Congo,  172 
Peculiarities  of,  at  Vivi,  Ponta  da  Leaha,  Gabun,  Loanda,  St.  Thomas, 

Nango,  172,  173 
at  Lado,  Nyassa  Lake,  173 
at  Guatemala,  174 

Regions  of  little,  in  eastern  and  western  hemispheres,  179 
west  and  east  of  Rocky  Mts.,  according  to  Loomis'  chart,  188 
Distribution  of,  in  Europe  and  Asia  affected  by  mountains,  189 


INDEX.  499 

Rainfall  in  South  America,  affected  by  the  Andes,  189 
on  eastern  coasts  of  Africa  and  China,  190 
Effect  of  small  easterly  or  westerly  wind  motion  on  the,  of  the  Andes 

and  Rocky  Mts. ,  from  30°  to  40°  latitude,  190 
Greatest,  in  Khasia,  204 
in  tornadoes,  399-401 

Pressure  caused  by,  in  thunder-storms,  465 
Redfield.     Observation  of  the  inclination  of  surface  winds  in  a  cyclone,  262 

Cyclones  preceded  and  followed  by  unusually  high  barometer,  first 

observed  by,  269 

Whirlwinds  produced  by  great  fires,  443 

Reese.     Appearance  of  the  spout  of  the  Lee's  Summit  tornado,  409 
Reed.     Rainy  and  dry  seasons  at  Greytown,  Nicaragua,  observed  by,  175 
Resultants  of  the  two  forces  and  motions,  71-74 
Reye.     Diameter  of  water-spouts,  408 

Ross,  Sir  James.     Table  showing  decrease  of  atmospheric   pressure  from  the 
tropics,  140 

Sand-spouts  and  dust  whirlwinds,  443-445 

Formation  of,  and  places  where  observed,  444 
hollow  on  inside,  445 

Scoresby.     Observations  on  sea-breezes  in  Greenland,  219 
Scott.     Thunder  storm  frequency  at  Valencia,  Ireland,  471 
Sea  and  land  breezes.     Special  treatment  of,  219 
Character  of,  195 

Dependence  of  the  strength  of,  on  the  nature  of  the  sur- 
face of  the  land,  195,  196 

Strongest,  along  coast  with  high  mountains  in  the  back- 
ground, 222 

observed  mostly  in  equatorial  and  tropical  latitudes,  219 
Effect  of  strong  prevailing  winds  on,  220 
True,  observed  in  calm  weather  only,  220 
Initiatory  action  of,  221 

Sea-breezes  have  greatest  strength  in  Jamaica,  199 
in  Greenland,  219 

Time  of  beginning,  maximum  and  end  of,  221 
stronger  than  land-breezes  in  equatorial  and  tropical  latitudes,  222 
along  the  coast  of  Guinea  observed  by  Com.  Burke,  222 
Sias,  Solomon.     Account  of  northers  in  Texas,  125-127 
Simoom  probably  a  dust  whirlwind,  445 

Sinclair,  Commodore.  '  Weather  under  the  cloud-ling  of  the  equatorial  calm- 
belt,  1 68 
Sirocco,  The,  336 

Reference  to  description  of  the,  by  Hahn,  337 
Skirtchly.     Account  of  a  water-spout,  414 
Smyth,  Prof.  Piazzi.     Remarks  on  dust  haze  at  Teneriffe,  129 


500  INDEX. 

Spitaler.     Normals  of  temperature,  100 
Squalls,  White,  436 

Bull's-eye,  437 

St.  Cloud  and  Sauk  Rapid,  Minn.,  tornado,  386 
Stockdale  tornado,  388 

Strachey,  R.,  Esq.,  Mountain  winds  in  the  Himalayas  observed  by,  223 
Sunsets,  Theory  of  the  red,  due  to  volcanic  ashes,  126 

Table  of  altitudes  and  corresponding  temperatures  and  pressures,  15 

of  observed  pressures  at  different  altitudes  indifferent  parts  of  the  earth,  16 
of  observed  rates  of  diminution  of  temperature,  34 

of  mean  annual  barometric  pressure  gradients,  and  annual  inequalities,  143 
of  mean  easterly  velocities  for  the  year,  January  and  July,  for  various  lati- 
tudes and  altitudes,  146 
by  Maury,  of    northern    limits   of  the  N.E.   trade-wind  in  the  Atlantic 

Ocean,  159 

showing  limits  of  the  trade-winds,  159 
of  the  limits  of  the  Pacific  trades,  162 
Dr.  Danckelman's,  of  rainfall  on  the  Congo,  172 
of  vertical  temperature  distribution  for  saturated  air  compared  with  that  of 

undisturbed  air,  232 

by  Ley,  showing  directions  of  surface  and  upper  winds  in  cyclones,  264 
of  J.  Allen  Brown,  of  inclination  of  winds  in  cyclones,  265,  266 
of  movement  of  cyclone  centres  by  Loomis,  276 
of  yearly  periods  of  cyclone  frequency  in  several  seas,  282 
Temperature,  Standard,  2 

The  absolute  zero  of,  4 

The  absolute,  4 

Table  of  diminution  of,  per  hundred  meters,  34 

Vertical  distribution  of,  causing  stable  equilibrium,  36 

Distribution  of,  over  the  earth's  surface,  98-101 

Effect  of  the  distribution  of  land  and  water  on  the,  at  the  earth's 

surface,  98 

Normal,  of  the  latitude,  99 
Table  of  normal,  for  different  latitudes,  99 
Average,  at    the  earth's  surface  for  the  northern    and  southern 

hemispheres,  100 
Average  rate  of  decrease  with  altitude  for  all  latitudes  and  the 

year,  100 

Difference  of  the,  gradient  in  winter  and  summer,  141 
conditions,  annual  inversion  of,  142 

Relative,  of  east  and  west  sides  of  the  continents,  179,  180 
Annual  ranges  of,  are  small  in  lower  latitudes,  182 
Effects  of  mountains  and  moisture  on,  189,  191 
Abnormally  high,  just  east  of  Rocky  and  Andes  Mountains,  192 
Summer,  of  high  plateaus,  198 


INDEX.  501 

Temperature,  Inversion  of  the,  with  the  altitude  in  winter,  345 

Sudden  changes  of,  in  thunder-storms,  451,  452 
Teneriffe,  Westerly  wind  at,  126 

Thermal  equator  or  the  maximum  of  temperature,  100 
Thunder-storms,  450-472. 

Observed  phenomena  of,  450-459 

Relation  of,  and   cyclones   as  observed  by  Klossovsky,  Aber- 

cromby,  Von  Bezold,  Davis,  Ferrari,  451 

Sudden  changes  of  temperature,  pressure,  and  wind  in,  452,  453 
Groups  of,  453 
Rain  areas  in,  454 
Composite  portraiture  of,  454 
Types,  Ferrari,  455 

Antecedent  and  following  phenomena  of,  455,  456 
Origin  and  form  of,  456 
The  theory  of,  459,  467 

Cause  and  results  of  pressure  gradients  in,  464-466 
Observation  of  pressure  gradient  in,  by  Clayton,  465 
Relation  between,  and  cyclones,  467-470 
Table  of,  in  Russia  by  Klossovsky,  469 
Location   of,    with   reference    to    cyclonic  areas.     Klossovsky, 

Hazen,  469,  470 

Annual  and  diurnal  inequalities  of,  470-472 
Time  of  occurrence  of,  on  land  and  sea,  471 
Winter,  at  Stykkisholm  according  to  Buchan,  471 
frequency  at  Valencia,  Ireland,  according  to  Scott,  471 
Greater  frequency  of,  on  land  than  on  the  ocean,  472 
Tomlinson.     Regularity  of  atmospheric  phenomena  in  the  calm-belt,  175 

Account  of  showers  of  fish  caused  by  water-spouts,  414 
Tornadoes,  347 

dependent  on  the  unstable  state  of  the  atmosphere,  348 

and  cyclones  compared,  347 

The  conditions  giving  rise  to,  348-353 

Vertical  distribution  of  temperature  and  pressure  in,  349,  350 

Vertical  circulation  in,  349 

Gyratory  circulation  in,  351 

Initial  gyratory  motion  of  the  air  necessary  for  starting,  351 

Smallness  of  the  effect  of  the  earth's  rotation  on  the  currents  of,  352 

Gyratory  velocity  and  its  effect  on  pressure,  353-362 

Law  of  gyratory  velocities  at  the  same  distances  from  the  centre  of, 

356 

Expression  for  the  centrifugal  force  of  the  gyratory  velocity  in,  354 
Isobaric  surfaces  and  gradients  in,  355 
Gyratory  velocity  within,  358 
Diminution  of  pressure  in  the  centre  of,  and  its  effects,  360 


5O2  INDEX. 

Tornadoes,  Instances  of  the  outbursting  of  confined  air  during  the  passage  of  the 
centre  of,  360 

Computation  of  outward  pressure  caused  by  the  passage  of  the  centre 
of,  over  confined  air,  361 

Friction  in  a  gyratory  circulation  necessitates  vertical  currents  in,  362 

The  energy  of,  362-371 

Maintenance  of  the  unstable  state  in,  363 

Thermal  energy  and  temperature  gradient  in,  363,  364 

Reduction  of  the  unstable  to  the  neutral  or  stable  state  in,  364 

Cause  of  the  first  motion  in,  365 

Relation  of  the  kinetic  energy  of  the  gyratory  velocity  and  the  poten- 
tial energy  due  to  pressure  in,  366 

Analogous  phenomena  in,  to  the  eye  of  the  cyclone  storms,  367 

The  greater  the  altitude  of  the  rarefied  centre,  the  more  violent  the, 
368 

Relation  of  the  height  to  the  diameter  of,  370 

Force  of  the  wind  and  supporting  power  of  ascending  currents  in,. 

371-395 

Theoretical  enormous  pressures  of  wind  in,  377 
Support  of  rain  and  hail  by  ascending  currents  in,  379-380 
of  Walterborough,  S.  C.,  381 
of  Wallingford,  Conn.,  382 
of  Mt.  Carmel,  111.,  383 

-  of  St.  Cloud  and  Sauk  Rapids,  Minn.,  385,  386 
of  Lee's  Summit,  386,  399,  407 
of  Irving,  387 

of  Stockdale  and  of  Delphos,  388 
of  Barnard  and  of  Gentry  County,  389 
Computation  of  the  enormous  velocities  and  pressures  of  wind  in,. 

389 

Width  of  the  path  of  destruction  of,  according  to  Finley,  390 
Velocity  and  lifting  force  of  the  ascending  current  in,  390 
Movement  of  bodies  carried  up  in,  391 

Explanation  of  the  lifting  power  at  the  earth's  surface  of,  393-395 
Resultants  of  gyratory  and  progressive  motions  in,  395-399 
Direction  of  the  rotary  motion  of.     Finley,  395 
Velocity  and  direction  of  progression  of.     Finley,  395 
Dangerous  side  of,  396 

Direction  and  relative  strength  of  winds  in  front  and  rear  of,  396,  397 
Dr.  Anderson's  account  of  direction  of  strong  winds  in  the,  of  April 

23,  1883,  397 
Difference  in  the  width  of  the  path  of  destruction  on  the  two  sides 

of,  399 

Rainfall  in,  399-401 
Cause  of  a  cloud  in  the  vortex  of,  402 
System  of  circulation  in,  403 


INDEX.  503 

Tornadoes  as  funnel-shaped  and  basket-shapea  clouds,  406 

Intermittent  action  of,  407 

Discontinuity  of  line  of  destruction  of  the,  of  April,  1883,  407 

Appearance  of  clouds  in,  410 

Appearance  of  the,  of  West  Cambridge,  410 

Plurality  of. spouts  in,  412 

Hail-storms,  420-429 

Movements  of  a  balloon  in  a,  observed  by  John  Wise,  425 

Fair-weather  whirlwinds  and  white  squalls,  434-437 

Where  they  are  most  likely  to  occur,  437-443 

Summer  and  afternoon  the   times   of  greatest  frequency  of,  according 

to  Finley,  441 

Toynbee.     Results  of  observations  on  winds  in  cyclones,  267 
Trade-winds.     See  under  Winds. 

Typhoons,  Doberck's  observations  of,  in  China  Sea  and  Philippine  Islands,  268 
Manilla,  of  Nov.  5,  1882,  as  investigated  by  Loomis,  295 

Vapor,  Aqueous,  of  the  atmosphere,  16 

The  amount  of  aqueous,  in  the  atmosphere,  19 

tension,  average,  at  the  equator,  101 

Effect  of  average  amount  of  aqueous,  on  the  density  of  the  atmosphere 

at  the  equator,  101 
Distribution  of  aqueous,  101 

Effect  of  the  aqueous,  in  expanding  the  atmosphere,  103 
Velocity,  The  gyratory,  in  terms  of  the  radius,  46 
Gyratory  and  centripetal,  55 

Gyratory,  increases  with  approach  toward  a  centre.     Examples,  55 
East  and  west  components  of,  108 
East  component  of,  increasing  with  altitude,  109 
Limits  of  the  east  components  of,  1 10 
Change  from  west  to  east  components  of,  114 
Annual  inequality  in  the  east  and  west  components  of,  115 
Of  the  east  and  west  components  depending  much  on  the  nature  of  the 

surface,  118 

Easterly,  deduced  from  pressure  and  temperature  gradients,  144 
Mean  easterly,  for  the  year,  January  and  July,  for  various  latitudes  and 

altitudes,  146 

Annual  inequality  of  easterly,  147 

Easterly  component  of,  at  various  points  on  the  earth,  148 
Venezuela,  Motions  of  the  clouds  at  Colonia  Tover  in,  123 
Vines,  Padre.     Observation  on  the  inclination  of  winds,  266 

Phenomena  attending  the  approach  of  cyclones,  302 
Remarks  on  pumping  of  the  barometer,  642 

Volcanic  ashes  carried  eastward  by  upper  air  currents.     Some  examples  of  this, 
123,  124 


504  INDEX. 

Wallingford,  Conn.,  tornado,  382 
Walterborough,  S.  C.,  tornado,  381 
Water-spouts,  401-420 

Formation  of,  401 

Cause  of  the  peculiar  outline  of,  402 

System  of  circulation  in,  403 

The  height  of,  408 

Diameters  of,    according    to  Horner,  Reye,   Loomis,  and  Judge 

Williams,  408 

Appearance  of,  on  land,  410 
at  sea,  413 

Account  of,  by  Sydney  Skirtchly,  414 
Formation  of  small,  on  seas  and  lakes,  and  description  by  Defranc 

and  others,  415,  416 

Observations  of  the  hollow  centre  of,  419 
West  Indies,  Steady  winds  from  the  east  at,  130 
Wilkes,  Capt. ,  Irregular  outline  of  the  atmosphere  surrounding  the  earth  first 

shown  by,  140 

Lower  temperature  in  the  calm-belt,  169 
Winds,  Relation  of  barometric  gradient  and  velocity  of,  85 
Prevailing  westerly,  at  elevated  mountain  peaks,  126 
Directions  and  relative  frequencies  of,  at  Pike's  Peak,  126 
Westerly  tendency  of,  near  the  earth's  surface,  113,  129 
in  the  interior  of  North  Africa,  129 
Average  velocity  of,  for  United  States,  Northern  Europe,  Southern  Asia, 

and  West  Indies,  130 

Remarks  of  Mr.  Laughton  on  westerly,  in  both  hemispheres,  140 
Surface,  149-154 
of  the  polar  regions  in  the  northern  hemisphere  having  a  component 

from  the  pole,  152 

Components  of,  in  northern  and  middle  latitudes,  152 
Components  of,  near  the  equator,  152 
Consequences  of  deflection  of,  due  to  land  barriers  on  various  portions  of 

the  earth,  183-185 

Charts  of,  by  Coffin  and  Brault,  186 
Effect  of  the  Himalaya  mountains  on,  186 
Effect  of  the  Andes  on,  187 
Effect  of  the  African  Mountains  on,  186 

Effect  of  the,  on  the  Pacific  and  Indian  Oceans  on  bordering  lands,  186 
Table  of  directions  of,  observed  in  summer  on  the  Indian  Ocean  accord- 
ing to  Woeikoff ,  205 
on  west  coast  of  Africa,  213 
Mountain  and  valley,  223 

Mountain,  in  the  Himalayas  observed  by  Strachey,  223 
Terrific  diurnal,  in  western  Thibet,  223 
Mountain,  on  Grey's  Peak,  Colorado,  224 


INDEX.  505 

Winds,  Diurnal  change  in  direction  of  T  in  Missouri  and  Kansas,  224 
Definition  of  the  force  of,  373 

Equation  for  converting  velocities  into  pressures  of,  377 
Observed  force  of,  in  tornadoes,  381 
Blasts  of,  and  oscillations  of  the  wind-vane,   446,  447 
Effect  of  blasts  of,  on  the  barometer,  449 
Wind-spouts,  418  ^ 

Wind,  trade,  Table  showing  the  northern  limits  of  the  northeast,  in  the  Atlantic 

Ocean,  158 

Table  of  the  mean  polar  limits  of  the  northeast  and  southeast,  159 
Table  of  the  equatorial  limits  of  the  northern  and  southern,  160 
Annual  oscillation  of  the  limits  of  the,  160 
Remarks  on  limits  and  progress  of  the,  161 
Table  of  limits  of  the,  in  the  Pacific  Ocean,  162 
Williams,  Judge.     Diameter  of  spout  in  Lee  Summit  tornado,  408 
Wise,  John.     Movements  of  a  balloon  in  a  tornado  cloud  observed  by,  425 
Woeikoff.     Tables  of  trade-winds,  158 

Chart  of  the  zone  on  which  rain  falls  in  the  course  of  the  year,  166 
Remarks  on  winds  of  south  central  Europe,  185 
Table  of  wind  directions  observed  in  summer  on  Indian  Ocean,  205 
Woodruff.     Investigation  of  cold  waves  in  the  United  States,  323-325 
Work,  Definition,  measure  and  unit  of,  20-23 
The  equivalent  of,  23 

Zi-ka-wei,  Directions  and  frequency  of  the  cirrus  clouds  at,  122 


f 


14  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 

LOAN  DEPT. 

This  book  is  due  on  the  last  date  stamped  below,  or 

on  the  date  to  which  renewed. 
Renewed  books  are  subject  to  immediate  recall. 


USep'638C 


LD  21A-50?n-ll,'62 
(D3279slO)476B 


General  Library 

University  of  California 

Berkeley 


